Occidental Petroleum Corp. said yesterday it was considering making a new offer for Cities Service Co., just hours after it dropped a $3.8 billion bid for the company because Cities rejected it.

"Occidental is continuing to study other possible courses of action with respect to Cities Service, which could include making another proposal to Cities Service or a tender offer for Cities Service shares," Occidental said in Los Angeles.

Cities Chairman Charles J. Waidelich replied that the company would be willing to listen to a new Occidental offer. "Cities and I reiterate our desire to discuss revision" of the previous bid, Waidelich said in a letter to Occidental Chairman Armand Hammer.

On Monday night, Cities' board unanimously rejected Occidental's $50-a-share bid for the company, which has been frantically seeking a buyer since Gulf Oil Corp. suddenly dropped its $4.8 billion, $63-a-share bid for Cities on Aug. 6. Cities also turned away a slightly modified version of Occidental's offer that did not change the price.

Occidental had offered on Friday to pay $50 a share cash for half of Cities' stock and then exchange securities worth roughly $50 a share for the remaining 38.2 million shares. Although the offer was considerably below Gulf's, analysts said it almost would have bailed out speculators who bought Cities stock at $50 or $55 a share in hopes of getting Gulf's price. Cities stock closed on the New York Stock Exchange yesterday at $37.625, up $4.375.

In rejecting Occidental's offer, however, Cities invited the company to make a revised bid. At the same time, it said it was continuing to talk with other potential buyers.

Warren Shimmerlik, an analyst at Merrill Lynch Pierce Fenner & Smith, said it was unclear whether Cities was close to receiving an offer from another suitor. "It's sheer speculation to suggest that they turned this offer down solely because they felt that someone they were talking to was about to come through," he said.

He added, however, "I would imagine everybody at their investment banking house is running around trying to find a buyer."

Cities has been seeking a new suitor since Gulf dropped its offer, citing antitrust objections to the proposed merger from the Federal Trade Commission. Cities, which filed a $3 billion breach-of-contract suit against Gulf, then said it would liquidate itself if it could not find another buyer.

A merger of Occidental and Cities would combine the nation's 12th- and 19th-largest oil companies into a company with $23.6 billion in sales in 1981, ranking it eighth among oil companies and 12th among all U.S. industrial firms.

If it acquired Cities, Occidental would gain badly needed domestic oil and gas reserves -- reducing its heavy dependence on sometimes unreliable foreign sources of oil -- and a 6,000-station gasoline marketing network.