It was more wishful thinking than fact, especially at the Republican National Committee. The rumor circulating on Capitol Hill earlier this week, that Sen. Charles McC. Mathias had changed his mind about retiring, had no basis in fact. Republicans are expected to lose his Maryland seat in November. The short-lived rumor was the result of a Mathias joke at the closed Wednesday luncheon of moderate-liberal Republicans who met in the office of Sen. Dan Evans.

Mathias suggested he would run for reelection if he could get conservative GOP Sen. Strom Thurmond to put in writing that he would give up the chairmanship of the Judiciary Committee to take over the Armed Services Committee. Mathias and other liberal Republicans have often said Thurmond stayed on Judiciary just to keep Mathias from becoming chairman.

Thurmond is in fact expected to move to Armed Services. And Sen. John Warner, who was in line to become chairman of that committee if the Republicans retain control of the Senate, reportedly is dismayed at Thurmond's decision. It was while the senators in Evans' office were discussing Thurmond's decision to change committees that Mathias make his joking remark. As a Mathias staff aide grumbled yesterday: "It was just a joke."

King Hussein's U.S. Visit

Jordan's King Hussein is on a whirlwind visit to the United States that will include attending the high school graduations of his twin daughters, a medical checkup at the Cleveland Clinic and a meeting with President Reagan. He arrived in Boston Wednesday with Queen Noor, his fourth wife.

The king is expected to speak at both graduations over the weekend. His daughter Princess Zeim, 18, will graduate from Westover School in Middlebury, Conn., Friday; and her twin, Princess Alisha, graduates from Dana Hall School in Wellesley, Mass., Sunday. Hussein is scheduled to meet with President Reagan Monday and later to have lunch with Vice President George Bush. Then after his trip to Cleveland, he is to return here Thursday to meet with members of Congress.

End Notes

Novelist and screen writer Mario Puzo, whose book "The Godfather" was turned into two film classics, has signed a contract to write still another movie, "The Godfather, Part III," Paramount Pictures announced yesterday. Author and former New York Times reporter Nicholas Gage, who will produce the film, said he hoped filming could begin next spring. There was no indication that director Francis Coppola, who was the creative influence behind the first two "Godfather" films, would participate in this one. Nor was there any indication what the story line would be . . .

British singer Petula Clark was driving around in nearby West Virginia this week looking at small towns in the Elkins area as part of her research for a musical she is writing. She was also in the area in January doing research for "Amen," the story of an Englishwoman who comes to the United States at the end of the Civil War and settles in a West Virginia village. She expects to open the musical, which is almost completed, in London next spring. Why West Virginia? Clark said, "I liked the sound of 'West Virginia.' It seemed to be right and it gave me the opportunity to mix in gospel and mountain music without sounding incongruous" . . .

Sen. Gary Hart is expected to show up this morning on the roof terrace of the Hotel Washington, where a film company is shooting "Deceit," starring Gene Hackman, Howard Duff and Kevin Costner. The film company, which is headquartered at the Bristol Hotel while in town, will be filming at several locations here until the end of the month . . .

Television producer Nancy Dickerson and public relations consultant Joe Canzeri have signed a contract with the U.S. Capitol Historical Society to produce a one-hour television film on the Capitol in conjunction with the 1987 bicentennial of the Constitution. Fred Schwengel, president of the society, said yesterday in a burst of hyperbole, "We expect our program in cassette form to be as common on the shelves of homes, libraries and schools as is the dictionary." Schwengel, incidentally, celebrated his 80th birthday last week by getting up in the morning to do 1,009 push-ups. He does that many every morning. For those who refuse to believe he can do that many push-ups, he invites them to the gym to count . . .