Texaco Inc. and Pennzoil Co. are discussing a possible settlement of the record $10.53 billion judgment imposed on Texaco, a federal judge in New York said yesterday.

Neither company would discuss the status of the case, apparently on orders from U.S. District Judge Charles L. Brieant, whose court is in White Plains, N.Y.

At a hearing yesterday, Brieant said, "The attorneys have informed the court informally that their clients are still having discussions with each other looking towards the amicable settlement and disposition of all of the underlying litigation. . . . "

The judge then adjourned the hearing, which concerned opposing motions by Texaco and Pennzoil involving appeals to the $11.1 billion judgment -- including accured interest -- against Texaco. That enormous award was ordered by a Texas jury last month after it found that Texaco had unethically interfered with an agreement by Getty Oil Co. directors to sell a major portion of the company to Pennzoil almost two years ago.

Texaco now owns all of Getty Oil. The award was the jury's assessment of the value of that loss to Pennzoil, plus punitive damages and interest.

Texaco attorneys argued at a Texas court hearing this month that Pennzoil's loss was no more than $500 million. Top officials of both companies have expressed a willingness to discuss a settlement. And investment bankers and financial analysts believe that Pennzoil might agree to take the billion barrels of Getty oil from Texaco that it had hoped to acquire two years ago.

According to one common theory, Pennzoil could pay Texaco $3.5 billion for the oil -- which has a current value of about $5.5 billion -- thus gaining both the oil and the equivalent of a $2 billion after-tax profit on the exchange. However, neither Texaco nor Pennzoil has publicly discussed what their negotiating positions would be.

The issue in Brieant's court is whether Texaco should be protected from claims on its assets by Pennzoil during the entire appeals process, which could go on for months if there is no settlement. Brieant adjourned the hearing on that issue until either side requests a new appearance in court.

"Of course, it would be my hope that it would not be" requested, he said.