The Spaniard, who was Swansea's top scorer last season with 22 goals in all competitions, has not featured for Michael Laudrup's men since damaging his ankle ligaments in the 1-1 draw at Norwich City last month.
Michu underwent surgery to remedy the problem and, although the former Rayo Vallecano man has not suffered any setbacks in his recuperation, he is not expected to return until next month.
And while the 27-year-old is pleased with his progress, he will not rush himself back into action.
"I am improving a lot," Michu told the club's official website. "I have started running and although I'm in a little pain I am happy with my progress.
"I want to be play as soon as possible. I am desperate to play because I am happy when I am on the pitch.
"With this injury, though, you need to be careful and see how the ankle is every day so I don't want to say, 'I want to be back for this date or game'.
"If I am going to play I need to be 100 per cent and not just 60 per cent. I want to be fit and I want to play at my highest level, so we will wait until I am fully fit."
