NEW YORK (AP) _ Davey Johnson said Saturday he disagrees with a published report that he would quit as manager of the New York Mets unless he receives a contract extension.

The New York Times reported Saturday that Johnson, who had the Mets in second place in the National League East, 2 1/2 games behind the St. Louis Cardinals going into Saturday's games, has intimated to friends that he does not want to run the team next season as a lame-duck manager.

He is in the second year of a three-year contract and, according to the newspaper, the Mets have not been willing to extend the contract.

Johnson said, ''I have read the article and I disagree with a lot of the things that are in there. It's true that I would like to have it renegotiated, and it's also true that we've had our differences, but I don't think it's anything that can't be worked out.''

General Manager Frank Cashen, who hired Johnson prior to the 1984 season, elevating him from Tidewater of the International League, confirmed that Johnson did ''broach the subject'' of a contract extension.

''I really don't have any comment on it,'' Cashen said Saturday. ''I'm trying to win a pennant, not negotiate somebody's contract at this time. You can take all the quotes that were in that story and apply them to last season.''

''All I want to do is win this pennant and we'll see what happens after that.''