DAMASCUS, SYRIA, SEPT. 16 -- Syrian Foreign Minister Farouk Charaa will meet later this month in New York with Secretary of State George P. Shultz as part of an intensified effort to end nearly a year of diplomatic estrangement between the two nations, a senior official here said.

The official, maintaining Syria's denial of any terrorist involvement, said that he is "optimistic" about the new attitude of the Reagan administration toward Syria. He added that a 10-month period during which U.S. Ambassador William L. Eagleton Jr. was withdrawn from Damascus gave both countries an opportunity to reevaluate "how to deal with each other."

Eagleton returned earlier this month and presented what Syrian officials described as a "warm and friendly" letter from President Reagan to Syrian President Hafez Assad.

The meeting between Charaa and Shultz on Sept. 29, during the opening of the United Nations General Assembly, is expected to dwell on the limited sanctions that remain in place against Syria.

"Mr. Shultz has asked for a meeting in New York and we welcome the idea," the official said.

The Reagan administration imposed the sanctions and recalled Eagleton after British authorities established that Syrian diplomats and intelligence officials had been involved in an aborted plot to place explosives aboard an Israeli jumbo passenger jet in London in April 1986.

Syria has steadfastedly denied involvement in the plot, and has blamed Israel for staging the attempt in order to embarrass Syria.

Britain broke diplomatic relations with Syria over the episode.

The senior Syrian official said in an interview that British officials sought earlier this year to reopen discussions with Syria about restoring relations, but he added that the overture was rebuffed.

"They have approached us since the beginning of this year," the official said, "but we say they have to apologize -- they have to express that they have made a big mistake."

Diplomatic sources in Europe have said Britain is considering a move to restore relations, but is still demanding that Syria punish the intelligence officials involved in the bombing attempt.

The U.S. decision to return its ambassador here, and to lift an embargo against American oil firms working in Syria, is based on an assessment that neither Syria nor the terrorist organizations with offices here have been involved in terrorist activity for the past 12 months.

"I think we've got Syria now about as clean as it's ever been on terrorism," said one western diplomat here.

U.S. officials said a key factor in Eagleton's return was Syria's decision to close a "liaison" office operated by the Abu Nidal terrorist group. The group is believed to be responsible for some of the bloodiest terrorist attacks in Europe and the Middle East in recent years.

The remaining U.S. sanctions -- including lengthy security checks for Syrian citizens requesting visas to travel to the United States and a ban on export credits for grain sales -- are expected by western diplomats to be at the top of the agenda for Shultz's meeting with Charaa.

"The sanctions are now an irritant to Syria," one western diplomat said. "They see them as completely unjustified because they've taken the position that they have done everything we wanted them to do."