Transportation Secretary Drew Lewis, one of the most highly regarded members of the Reagan cabinet, is considering an offer to run Warner Amex Cable Communications Inc., industry sources said today.

The cable system operator, a partnership of Warner Communications Inc. and American Express Co., has been seeking a new chairman for some time. Three weeks ago, the current chairman, Gustave M. Hauser, announced plans to leave the post, to pursue "certain private investment opportunities." Sources say, however, the search for a new Warner Amex chief executive began weeks before Hauser's announcement.

Spokesman for the two companies declined substantive comment on the offer to Lewis. Linda Gosden, director of DOT's Office of Public Affairs, said Lewis has been "contacted by a number of companies" but wouldn't name them, or comment on Lewis' intentions.

Lewis' future plans have been the subject of considerable speculation in Washington political circles. At various times during his two-year cabinet stint, he has been reported to be moving to the White House staff, the Office of Management and Budget, and the Republican National Committee.

Lewis, however, has made no secret of his intention to return to the private sector after two years of government service.

Word of the decision facing Lewis comes as he is mired in a political fight to get Congress to pass the administration's proposed five-cent increase in federal gasoline tax, an effort Lewis has spearheaded.

Warner Amex is considered one of the most technologically innovative and politically savvy companies in the cable television business. In 1977, it became the first cable company to offer two-way or interactive services and the so-called "Qube" system in Columbus, Ohio, has been the centerpiece of successful Warner Amex efforts to win cable franchises in major cities like Houston, Cincinnati and Pittsburgh.

But after victories in the highly politicized franchise competition, Warner has faced the increasingly costly task of constructing the cable systems. Warner Amex, despite the wealth of its two parents, is struggling with losses reportedly more than $20 million this year and despite sharp revenue gains to more than $300 million, officials of the two companies are increasingly wary of the operation's drain on their resources.

The cable systems themselves serve more than 1.1 million subscribers, which makes the firm the sixth largest operator in the industry.

It is clear that the search for a successor to Hauser, widely regarded as a cable industry innovator, has focused on executives primarily outside the company with experience in both the political and corporate management worlds, with an eye toward finding a chief executive with a "trouble shooting" background.

Lewis, 51, would seem to fit the bill. A former deputy chairman of the Republican National Committee and worth almost $3 million at the time of his Senate confirmation almost two years ago, Lewis has helped turn around several large companies with financial problems and subsequently ran a Pennsylvania management consulting firm advising firms with comparable difficulties.

As a chief executive, he was widely thought to have helped streamline and turn around Simplex Wire & Cable Co. and Snelling & Snelling Inc, the employment agency.