A new round of rumors that Sen. John P. East (R-N.C.) may retire before the second session of Congress opens on Jan. 21 swept through Washington and his home state yesterday, and were denied again by the ailing senator's close associates.

R.E. Carter Wrenn, director of the National Congressional Club, the Raleigh-based conservative organization that supports East and his mentor, Sen. Jesse Helms (R-N.C.), said he had spoken to East yesterday afternoon and "he told me there's nothing to it."

East's offices in the Capitol and in five North Carolina cities were closed or not answering phone calls yesterday and the senator could not be reached directly.

East announced last September that he would not seek a second term in 1986. Stricken with polio 30 years ago, East, now 54, has been hospitalized at least three times this year for hypothyroidism, a malfunction of the thyroid gland, and related symptoms, causing prolonged absences.

The most recent announced hospitalization, which began Nov. 18, was for a low white-blood-cell count, his office said. He missed many of the final votes of the year but made it to the Senate Dec. 18 to vote for the conference report on the agriculture bill that came out of Helms' committee.

East said when he announced his retirement plans that he would serve through the end of the 99th Congress, but fresh rumors of early resignation plans were reported by several sources in North Carolina and in the Capitol yesterday.

They may have been triggered by a speculative item in the current Newsweek magazine, suggesting that Senate Majority Leader Robert J. Dole (R-Kan.) "would not mind" if East stepped down in favor of someone who could be present to vote more regularly.

A longtime conservative leader in North Carolina said he had heard rumors that East's staff had been advised to circulate resumes and even that a moving van had been hired to move the senator and his family home to Greenville, N.C. "I've got to the point I don't believe anything," he added.

Another source said he had been told that East may resign early next month, on the fifth anniversary of his swearing-in, when he would qualify for a minimal federal pension.

Tim Pittman, press secretary to North Carolina Gov. Jim Martin (R), said he had been fielding press calls about the rumored resignation all day. The governor is on vacation and has received no communication from East, Pittman said.

A spirited battle to succeed East is under way. Rep. James T. Broyhill (R-N.C.) is considered the favorite for the seat but faces opposition in the Republican primary from David Funderburk, a Campbell College, N.C., professor and former U.S. ambassador to Romania. Funderburk is backed by the National Congressional Club. No clear Democratic favorite has emerged.

Martin, though a longtime ally and former House colleague of Broyhill's, has announced he will be neutral in the primary. Sources close to the governor said that if East resigns before the May 6 primary, Martin would likely appoint an interim senator who would serve only for the balance of East's term.

Speculation about such an appointment has centered on former governor James Holshouser (R), who has health problems requiring regular kidney dialysis, and state GOP chairman Robert Bradshaw.

A Reagan administration official who has monitored the situation said he has been told that the National Congressional Club does not welcome either Bradshaw or Holshouser and has not been able to get assurances from Martin that he would name anyone more to Helms' liking.

This official said East is likely to serve as long as his health permits, but may come under new pressure to step down after the Republican primary in order to allow Martin to name the winner as interim senator, giving him a head start on the November race.