The Spain international has been out since December after having an ankle operation and could make a welcome return in their fifth-round tie against the Toffees
The Spain international has not featured for the Welsh outfit since a 1-1 draw at Norwich City in December after suffering ankle ligament damage, for which he underwent surgery.
Swansea's form has dwindled in the absence of last season's top scorer, though new head coach Garry Monk has overseen a victory over rivals Cardiff City and a draw at Stoke City in his first two matches in charge, and Monk's tenure could be further boosted by the return of the 27-year-old.
"He [Michu] is training today and we'll see how he feels," he told reporters in a press conference on Friday. "If he feels fine then maybe he'll play a part on Sunday."
Everton boss Roberto Martinez is a former team-mate and manager of Monk from the Spaniard's tenure at Swansea, and Monk says he is looking forward to the reunion.
"I got to form a really good bond with him when he was here," he added. "I've learnt a lot from him and he is great guy at the top of his game right now.
"It will be good to see him and his staff as well. We keep in contact and I'm sure that relationship will always be there."
After collecting the Capital One Cup trophy last season, Monk is keen to experience glory in the FA Cup, insisting they will go out to win.
"We had a good experience in a cup competition last year, and we'll be trying to win the game," he said.
"But we have to approach it how we want to and do the best we can. The competition has massive history and all the players will be aware of it growing up and one they look forward to playing in."