Mobil Corp. may follow on the heels of Exxon and withdraw from its operations in Libya.

Exxon said Thursday it was cutting all ties to Libya and would withdraw its personnel, a step the U.S. government has urged the six American oil companies operating there to take. Yesterday a Mobil statement said, "We can confirm we have been in discussion with the Libyan authorities with regard to our operations in the country. We are studying the entire situation."

Mobil has a total of 134 employes and dependents living in the country; about 100 are Americans. Another 150 employes work there on a rotating basis, the company said.

Mobil stopped oil production in Libya on Nov. 1. At one point it had a production-sharing agreement with the Libyan government under which it was producing 100,000 barrels a day, about 30,000 for Mobil.

The Reagan administration is reviewing ways in which it can bring pressure on the Libyan government of Muammar Qaddafi to halt its military and political operations in other African nations. High on the list of some U.S. officials is getting all of the American oil companies out of Libya, a move that could put new economic pressure on Qaddafi.

The other companies operating there, Occidental Petroleum, Marathon Oil Co., Conoco and Amerada-Hess Oil Co., have given no hint they are considering a withdrawal. The latter three companies, along with the Libyan National Oil Co., comprise the Oasis Group, which currently is producing about 200,000 barrels of oil daily.

A Marathon spokesman yesterday would say only that his company is "keeping apprised of the situation on a daily basis."