The Spanish attacker has returned to training but will not be fully fit in time to face Rafa Benitez's side, though he could be available for Sunday's trip to Liverpool.
The Spanish forward has not featured since December, when he underwent surgery to resolve a problem that had hampered him since the start of the season.
Michu has returned to training and Garry Monk had hoped he would be in contention for the first leg of the round of 32 tie, but the head coach has revealed the former Rayo Vallecano man will play no part at the Liberty Stadium.
"The last two days, he (Michu) has reacted well," Monk told a press conference on the eve of the clash with Rafa Benitez's side. "He had a slight bit of swelling and that's the only thing which has kept him back.
"He had got to a good level with his rehab and was just about to go back into full training when his ankle swelled up a little bit.
"So we had to pull him out for a couple of days, but these last couple of days, he has been building it up again and he should be back in full training by Friday."
Michu scored 22 goals in all competitions last season and the 27-year-old has been sorely missed by the Welsh club.