On Monday, Mike Puma of the New York Post noted the Mets are "keeping surveillance" on the Girardi situation as they seek a replacement for Terry Collins, who resigned following a 70-92 season.
A source told Puma the Mets "fully expect" the Yankees to retain their manager, but he would be considered by general manager Sandy Alderson if he becomes available.
Girardi said Sunday he isn't overly concerned about his future and would let the Yankees decide how to move forward after the campaign ends, per Mike Mazzeo of the New York Daily News.
"I'm never worried about that. I've never worried about his future. I worry about other people's futures, but not my own," he said. "I believe the man upstairs is in charge of me, and whatever happens, happens.
"I think an organization has to do what they're comfortable with, right, and it may not always agree with the person that is either being fired or however it goes. But I think that's Hal [Steinbrenner] and Brian [Cashman's] decision. Whatever their decision is, you know, I'll live with it."
Girardi came under intense scrutiny for failing to challenge a key play in Game 2 of the team's ALDS matchup with the Cleveland Indians. Replays showed the call should have been a foul-tip strikeout on Lonnie Chisenhall rather than a hit-by-pitch, and Francisco Lindor proceeded to hit a grand slam for the Tribe.
The Yankees went on to lose the game in extra innings, but they have bounced back to win the next two contests to level the series at 2-2. The decisive Game 5 is scheduled for Wednesday night in Cleveland.
In the bigger picture, Girardi has accumulated a 910-710 regular-season record across 10 years as the Yankees manager. He led the storied organization to its 27th World Series title in 2009.