Paul Thayer, an aerospace executive who has said the military must join in holding down government spending to resuscitate the economy, is expected to be named deputy secretary of defense, Pentagon sources said yesterday.

Thayer, chairman and chief executive officer of the LTV Corp. of Dallas and chairman of the U.S. Chamber of Commerce, discussed the No. 2 job at the Pentagon yesterday morning in a 45-minute meeting with Defense Secretary Caspar W. Weinberger.

Sources said Weinberger urged Thayer to become his deputy, replacing Frank C. Carlucci, who plans to leave government in a few months. Carlucci, who has told friends he must return to private life for financial reasons, has been interviewed by several firms but has not announced where he intends to go.

Asked if President Reagan would nominate Thayer as deputy defense secretary, assistant White House press secretary Anson Franklin answered, "No comment," as did LTV spokesman Julian Scheer.

Weinberger, like several of his predecessors, has relied on the deputy secretary to run the vast Pentagon bureaucracy. This includes reviewing multibillion-dollar weapons programs and recommending which should be approved or canceled. This gives the defense secretary time to wrestle with policy issues within the Pentagon and the Cabinet at the White House and to testify before Congress.

Thayer, who will be 63 next week, is credited with pulling the LTV conglomerate back from the brink of bankruptcy.

A pilot, he still performs acrobatics in jet airplanes, shoots par golf and is well known in the aerospace industry. The Vought Corp., which makes the A7 attack plane, is among LTV's subsidiaries.

Thayer told Reagan in a White House meeting early this year that the Pentagon could save money by procuring less expensive weapons. He also has repeatedly warned that national economic problems require that defense share in government budget-trimming.

"The time has come for Congress to get serious about controlling federal spending," Thayer said in a speech prepared for delivery to the Youngstown, Ohio, Chamber of Commerce last night. "The business community must pull together on this issue and urge Congress to leave no area of the budget untouched. That includes defense, the big entitlement program and Social Security.

"We simply can't go on piling up debt which drains capital from the private sector and drives up interest rates," Thayer added, endorsing a basic tenet of Reagan's economic policy. "No effort means more to the jobless than cutting the rampant growth of spending and deficits."

Thayer's exhortations on holding down defense spending would appear to conflict with Weinberger's unbending opposition to limits on the increases he has requested in the Pentagon budget.

"This wouldn't be a problem for Paul," said a source who knows Thayer well. Like Weinberger, he said, Thayer has spoken out for a stronger defense while encouraging efforts to get more bang for the taxpayers' bucks.

Another high-level departure at the Pentagon will be Jack R. Borsting, the controller. A holdover from the Carter administration, Borsting intends to depart around Christmas and will head the University of Miami's business school.