Cashman also said he spoke to the agent for free agent third baseman Scott Rolen and said he is interested in luring former Atlanta Braves third baseman Chipper Jones out of retirement.
"If Chipper wants to come back, I would love to have Chipper," Cashman said via ESPN New York.
Jones' agent, BB Abbott, said Jones chuckled after seeing Cashman's comments on Twitter and intends to stay retired.
Lee, 37, who did not play last year, is reportedly interested but has not made a decision. He batted .267 with 19 home runs in 113 games in 2011.
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Outfielder Ben Francisco was released by the Cleveland Indians, then signed a minor-league contract with the Yankees later in the day, the New York Post reported.
Francisco played for three Major League teams last season - Houston, Toronto and Tampa Bay - and combined to hit .240 with four home runs.
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Los Angeles Dodgers pitcher Zack Greinke was scratched from his scheduled start because of a sore right elbow, but after he was examined by a doctor in Los Angeles, it was determined the injury is not serious, Hardball.com reported.
Greinke was diagnosed with inflammation in the back of his elbow, and is expected to resume throwing after 2-3 days of rest.