Swansea manager Garry Monk says Michu's contract could be terminated if the Spaniard does not find a new club before the end of the transfer window.
The 29-year-old's current deal expires next summer and he has not played for the Swans since April 2014, spending last season on loan at Napoli.
The summer transfer window closes at 18:00 BST on Tuesday, 1 September.
Asked if the Swans and Michu could part by mutual consent if no other club can be found, Monk replied: "Possibly".
"But hopefully we can sort something out before that and I know Michu wants that himself and the club does as well.
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"It's working together you know. It's not done in any negative way it's done in a positive way."
Michu has been linked with a move to Celtic this summer, but no transfer has been agreed.
The Spain international played only five games in the 2014-15 season because of injury problems.
Monk admitted Michu could still be a Swansea player when the transfer deadline passes.
"There's always a possibility. He's not part of my plans going forward. Michu made his decision last season to try and go on and further his career elsewhere and it's the same situation now.
"Whether the window shuts it's an ongoing situation where we're trying to find the right solution for him.
"We want the best for him because we're very thankful for what he's done for the club.
"He contributed in the seasons he was here but we've moved on now, the squad has moved on and it's about finding the right solution for himself and for the club."
"It's just about trying to come up with that solution that suits both parties."