Be it ever so humble, there may be no place like aging Boston Garden

Few Bostonians are more avid sports fans than Mayor Raymond L. Flynn, who nearly two decades ago came within inches of a professional basketball career. But despite his continuing enthusiasm for the game, and especially for the Boston Celtics, it is questionable how far he will go to help provide the team with a new arena.

Without strong Flynn leadership, a recent proposal to build a new arena is just another case of ''pie in the sky.'' If there is to be a new arena, the mayor will be an essential player in the working out of a financing package.

Delaware North, which owns Boston Garden and the Boston Bruins professional hockey team, wants no part of a new arena. The firm prefers upgrading the Garden , provided that a satisfactory agreement - presumably including tax concessions - can be worked out with the city.

Such a renovation, which clearly would cost a lot less than the estimated $78 .9 million for a larger new structure, might not be all that great a bargain, however, for either Boston or the sports fans attending games there. It still would be an old building, with some obstructed seats and other limitations.

The latest arena proposal was produced by consultants who conducted a feasibility study for the Massachusetts Convention Center Authority (MCCA). As welcome as private development of a structure to replace six-decade-old Boston Garden would be, prospects for such a project seem slim.

Most of these indoor stadiums are largely, often entirely, publicly financed. That almost certainly would be the route taken here, as has long been recognized by those pushing for a new Boston arena. The big stumbling block has been agreeing on a politically acceptable way of paying for the project, which almost surely means increasing taxes. The latest proposal, endorsed by the MCCA, embraces hiking the 5.7 percent state hotel-motel room-occupancy tax to 8 percent.

That potential funding vehicle, however, can hardly be expected to appeal to Mayor Flynn, who wants to tap the same revenue source to help Boston keep its books balanced. The mayoral proposal, embraced in legislation filed for state lawmaker consideration in 1985, would increase the city's hotel-motel levy to 9 percent. Also sought are a new, 6 percent local entertainment tax, to be paid by those buying tickets to shows, concerts, and sporting events in Boston, and a 15 percent parking excise tax.

Since all three parts of the Flynn package are needed to raise the $45 million in revenue required to avoid further municipal employee layoffs and cutbacks in city services, the mayor can hardly be expected to be even mildly supportive of the arena project, as much as he might want to see the project go forward.

While at this point there is nothing to suggest that any kind of a Boston levy boost, regardless of its purpose, might be acceptable in the coming months, a lot of teamwork between city and state leaders might help to come up with funding for an arena project.

Already, less than muffled utterances of skepticism have been voiced from within legislative circles, especially by senators and representatives from outside Greater Boston, some of whom are concerned that their constituents might have to help pay for something that would perhaps benefit them little or not at all.

Lawmakers from central and western Massachusetts are quick to point out that the Springfield Civic Center and the Centrum in Worcester were built without leaning on state taxes. They are generally unconvinced that a new indoor stadium in Boston would generate enough growth in the state's economy to produce even a few extra dollars of potential local aid for their cities and towns.

And there is nothing approaching a consensus among Boston-area legislators on the feasibility of increasing the hotel tax, or for what purpose such funds would be earmarked.

If the MCCA and others who want the arena are to make much headway, they will have to get the support of Mayor Flynn and Gov. Michael S. Dukakis both for the project and the means of financing it.

As much as Mayor Flynn wants his revenue package, including the hike in the hotel-motel tax, for municipal coffers, he just might become amenable to modifications that could help get a new arena built. First, however, those promoting the project must convince him that a new, larger, indoor sports facility would be such a boon to the city's economy, both during construction and for years to come, that it is something he cannot afford to ignore.

To his credit, the mayor has not let his enthusiasm for sports, especially the Celtics, rush him into endorsing the MCCA proposal for a new indoor stadium on the site of the North Station alongside the present Boston Garden. The 17,300 -seat facility, atop a new underground railroad station with adjoining shops and restaurants, almost certainly would spur increased private development in the area. It should be noted, however, that the projected $141 million complex does not include off-street parking, which presumably would come later.

Drafters of the current proposal estimate a new arena could be ready for occupancy within five years, if legislative approval and funding were approved by next summer.

A better and perhaps fairer financing plan might involve anchoring the project through an entertainment tax. Such, however, would be paid substantially by those who attend games or events at the Garden and its successor, most of whom are residents of the commonwealth. The hotel-motel tax, on the other hand, hits mostly out-of-staters, which makes it a bit less distasteful to state lawmakers.

Although Delaware North could conceivably keep the Bruins in the present quarters, such an arrangement would appear impractical, since the Celtics and other renters of the Garden, such as the ice shows and circus, almost certainly would move to the new indoor stadium. The present Garden owners can be expected to do whatever they can to discourage the project, which would shift their role from landlord to tenant and end their control of the lucrative concessions business.