With the approval of President Carter, Jay Solomon, administrator of the General Services Administration, has decided to ask for the resignation of his top aide, Deputy Administrator Robert T. Griffin, The Washington Post has learned.

Reacting to federal and internal investigations that have disclosed widespread corruption inside GSA, Solomon has been trying in recent months to take control of the sprawling agency, which spends $5 billion a year to provide government workers with offices and supplies.

Solomon, administration sources say, has become convinced that he cannot effectively do so while GSA employes are unsure whether he or Griffin, a close friend of House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), is really in charge.

Because of his relationship with O'Neill, Griffin, 61 and a 35-year GSA veteran, has had his own base of power, particularly because of his contacts in Congress.

Solomon was named GSA administrator a little over a year ago only after O'Neill had unsuccessfully sought to have Carter select Griffin, then a high GSA official, to head the agency. Solomon's predecessor, Jack M. Eckerd, a holdover from the Ford administration, had resigned after Carter insisted he named Griffin as his deputy.

These incidents fostered the impression within GSA, sources said, that Griffin might be more powerful than Solomon. In addition during his first year at GSA Solomon delegated much of the authority for running the agency to Griffin. It was Griffin who alerted Solomon to internal GSA findings that the agency had been paying companies that did not exist for supposedly doing maintenance work in federal buildings here. Subsequent investigations by the U.S. attorney's office and the FBI have found that some GSA employes certified repair work in federal buildings that had never been done. In return, sources familiar with the probes say, the employes were given as much as $250,000 each in payoffs over a two-year period by the firms and individuals who were supposed to have done the work.

Similar practices are being uncovered by the U.S. attorney's office in Baltimore in GSAs purchasing of office supplies, sources have said.

As Solomon became determined to take charge, sources said, he has been told that his orders were being obeyed only half-heartedly because many employes remained loyal to Griffin and believed that he would outlast Solomon.

The split between the two men has been magnified by differences in style. Griffin from Somerville, Mass., has been known as an effective and well-informed administrator who was thought by some to be a heavy-handed official who represented the "old way" of doing things at GSA.

Solomon from Chatanooga, Tenn., is a former real estate developer who came to Washington thinking he would spend much of his time enlarging GSA's contribution in cultural areas and attending ceremonial functions.

But, as he became more concerned about the developing scandals in the agency, Solomon, 56, switched his attention to GSA's more basic functions and developed a reputation for dealing openly with the unraveling disclosure of abuses. He has expressed amazement at the way GSA conducts much of its business in comparison with his experience in private industry.

Last spring, Solomon appointed Vincent R. Alto, a former federal prosecutor known for his organized crime investigations, to supervise GSA's investigations of the abuses.

In recent weeks, Alto and Solomon have discussed Griffin and his future with President Carter and his top aides Hamilton Jordan and Jody Powell. While all the participants were said to have been in agreement that Griffin who makes $50,000 a year, should be asked for his resignation or of the decision before it was announced, according to sources. Beplaced on administrative leave pending his dismissal, Carter, at Solomon's suggestion, agreed to inform O'Neill cause O'Neill was not in Washington, yesterday the move was delayed until his return.

In the meantime, the White House yesterday issued a statement from Carter supporting Solomon and any "procedural, personnel, organizational and other actions" he might take to "bring this matter (the GSA abuses to light and to bring those responsible to justice."

The statement called corruption in government "intolerable" and said Attorney General Griffin B. Bell has been asked by Carter to make available any assistance Solomon might need during the investigations.

While the statement, addressed to Solomon and signed by Carter, does not mention Griffin, it was said to be intended to represent the "blank check" Solomon needed to ask Griffin to leave.

Solomon was out of town yesterday and could not be reached for comment. Griffin said he had not been told of the decision and doubted it was true.