Swansea chairman Huw Jenkins is set to meet Michu in the next few weeks to discuss the Spaniard's future.
Michu has recently had a second ankle operation and, says Jenkins, faces a "dilemma" over his future in the game.
Jenkins said: "We are going to meet the player and his representatives and see where he is at with his fitness and what he wants to do from January."
The striker, 29, has not played for the Swans since April 2014 and spent 2014-15 on loan with Serie A club Napoli.
Swans manager Garry Monk recently suggested the player's contract could be terminated if he did not find a club in the summer transfer window.
He was linked with Celtic, but no move materialised.
Michu joined Swansea from Rayo Vallecano for £2.2m during the summer of 2012 and was the club's top scorer with 22 goals in his first full season.
But the former Oviedo and Celta de Vigo player's second season with the Swans was marred by knee and ankle problems and he scored only two goals in 15 starts in the Premier League.
Jenkins was questioned on Michu's future at a meeting of the Swansea City Supporters Trust, at Liberty Stadium.
He later told BBC Wales Sport: "As a club we can't forget the fantastic service he gave us for that 18 months - we have to make sure we help him as much as we can, taking into account all the serious injuries he's had and the attempts he's made to get back to fitness."
The Swans chairman added: "It's a never-ending dilemma for people like Michu striving to get back to fitness and get back to the levels he was at.
"It's a difficult process and mentally it can be difficult.
"We just want to make sure where he is at and we will have that meeting over the next few weeks."
Jenkins also said that plans to expand the Liberty Stadium could cost them more than £50m.
The club are in talks with Swansea Council over planning issues and could eventually buy the stadium outright from the Council.