Jordan ready to join peace talks?

When it comes to the troubled Middle East, American diplomats have learned from hard experience not to set their sights too high. The current joke has it that the ''optimists'' in the State Department think there is only a 30 percent chance that King Hussein of Jordan will soon announce that his country is ready to join negotiations with Israel.

Actually, the optimists, and other officials, are a bit more bullish than that. As one State Department official puts it: ''Our view is that King Hussein is close to announcing his readiness to enter the process.'' American optimism is based on several factors:

* Despite criticisms of the United States made in Moscow recently by Palestine Liberation Organization (PLO) chairman Yasser Arafat, State Department officials say the latest meeting between Mr. Arafat and King Hussein showed that the two were dealing seriously with President Reagan's peace plan.

* A formula has been found for dealing with the problem of Palestinian representation in any talks with the Israelis. Members of a joint Jordanian-Palestinian delegation would appear without being publicly identified. This would offer a way around Israeli objections to any participation by PLO members or pro-PLO Palestinians.

* Hussein has been looking for signs that Mr. Reagan is serious about pursuing his peace initiative and that the American leader will try to obtain a freeze on new Israeli settlements on the Israeli-occupied West Bank of the Jordan River. Reagan has no magic formula for doing this. Officials say simply that the Israeli public might make it difficult for Israeli Prime Minister Menachem Begin to build more settlements if it meant undermining a chance for direct talks with Jordan.

But a State Department official adds that Reagan has assured King Hussein that he will ''push hard for a settlements freeze.''

Middle East specialists warn at the same time that much could go wrong in all this. A lot will depend on whether King Hussein, in announcing his willingness to participate in talks, also insists on preconditions before doing so. And some specialists say they are betting that Prime Minister Begin will not agree to a settlements freeze under any circumstances.