Negotiators seek this week to finalise a format and schedule for the debates, the best - and arguably the last - chance for Mr Dole to erode the President's lead in the polls.
Technically, Mr Perot's inclusion will be determined by the bipartisan Commission on Presidential Debates, according to various criteria. In fact it is an exquisitely political decision that must ultimately be settled in a deal between the Dole and Clinton camps.
The underlying assumption is that the billionaire Texan, this time running for the Reform Party, will split the anti-Clinton vote and make the President's re-election even more likely. The Republicans, therefore, want to keep him out; for exactly the same reasons Mr Clinton's advisers want Mr Perot in.
Thus far the haggling has got nowhere, while the commission's rules send mixed signals. On the basis of his 1992 performance, when as an independent he won 19 per cent of the vote, Mr Perot is receiving $30m (pounds 20m) of federal funds for his campaign. He is on the ballot in enough states to have a chance of a majority in the electoral college.
On the other hand, to qualify for the debates a candidate must be generating "significant national enthusiasm or concern". Mr Perot is languishing at 5 per cent or so in the polls, and what "national enthusiasm" exists has not exactly been fired by his choice of running-mate, the little-known economist Pat Choate.
And, say Republicans, if Mr Perot, then why not Ralph Nader, the consumer activist and Green Party candidate who is also on the ballot in many states? More pertinently, Mr Nader would probably draw votes from Mr Clinton, especially in California. Mr Nader says he should be included because he is "well known". But if he is, other fringe candidates like John Hagelin of the Natural Law Party, are bound to demand they take part as well.
As matters stand, the first debate will be in St Louis on 26 September (put back from 25 September, because Mr Clinton addresses the United Nations the previous day). Thereafter, according to provisional dates, another will be held in St Petersburg, Florida on 9 October and a final one in San Diego on 16 October, sandwiched around a vice-presidential match-up on 12 October in Hartford, Connecticut.
The Dole camp would prefer four hour-long debates instead of three 90- minute ones. Anxious to cash in on the popularity and speaking skills of his running-mate, Jack Kemp, the Dole camp wants two vice-presidential debates. But that will probably be rejected by the Clinton campaign.