The newspaper, which did not say where it got the information or provide details of the offer, said General Manager Brian Cashman had coffee with Girardi and met with his agent, Steve Mandell, over lunch this week.
Girardi, 48, has a 564-408 record in four seasons with the Yankees, including a World Series championship in 2009.
“We are going to give him a real good reason to stay,” Cashman said earlier this week in a news conference.
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