The International Monetary Fund's short-term loan funds would be exhausted by another loan approximating the size of the bail-out requested by Mexico now before the IMF, a private international finance research group said here yesterday.

In releasing a study on the IMF -- which recommends a major expansion of the agency's long-term lending potential -- economist John Williamson of the Institute for International Economics said that the Mexican situation shows that "the fund's short-term liquidity position is even tighter than we thought."

As part of an international aid package to Mexico, the IMF is considering a $4 billion conditional loan over a three-year period, plus about $800 million from a special IMF fund. Fund officials have indicated that they may not reach an agreement with Mexico -- which will have to promise specific economic reforms -- until October. An emergency credit of $1.68 billion is being put together as an interim measure by the Bank for International Settlements in Basel, Switzerland.

The institute's report, drafted some weeks ago for publication prior to the May 6 opening of the IMF annual meeting in Toronto, concluded that IMF quotas -- national currencies deposited by member countries--should be boosted from approximately $67 billion to $110 billion to enable the fund to deal with international loan needs in the latter half of the 1980s.

Relative to the size of the world economy, that would still leave the fund below capabilities agreed to when it was established in 1944, the report said.

The subject of the quota increase will be a major topic for the Toronto session, but negotiations on the amounts are not likely to be concluded until some time next year, with new quotas coming into effect in 1985. U.S. government authorities, sensitive to the difficulty of getting international financing appropriations through Congress, have been urging a much more modest expansion of quotas than those suggested by Williamson.

The international institute is funded by the German Marshall Fund of the United States and directed by C. Fred Bergsten, an assistant secretary of Treasury in the Carter administration.

Williamson, a senior fellow of the organization, former adviser to the IMF and consultant to the British Treasury, argues in the report that, despite world recession and a reluctance of private banks to finance Third World development, the IMF's lending role has dropped since the middle of 1981, excepting its huge, $5.75 billion loan of last year to India.

This trend comes "at just the time when it should be doing more," Williamson said.

He attributed a more tight-fisted approach in part to political pressures from the Reagan administration on the fund to tighten terms of its loans. Other causes cited by Williamson are a fund "judgment" that borrowing countries must themselves make a tougher adjustment to recession, and "some expression of concern by private banks that the fund's 'seal of approval' was losing its validity."

On balance, the report says that the terms of IMF lending have been "generally appropriate to the needs of its borrowers," and that there has been little evidence of excessively austere terms in a dozen cases studied, including Jamaica, Tanzania, and Turkey, where charges of such "overkill" had been made.

IMF Managing Director Jacques de Larosiere has acknowledged that the fund looks to more realistic adjustment policies by borrowing countries, but vigorously denies that the IMF has been responding to political pressures. He denies that the fund has move from standards that some thought were too easy a couple of years ago to standards that are now too tight.

"This is a misinterpretation," he said in a recent speech. "Actually, what has happened is that with the deteriorating conditions in the world economy over the past few years, the adjustment efforts required of countries have necessarily been that much more onerous and demanding."