The Spaniard has been sidelined since December after undergoing ankle surgery and the Swans were hoping he would be back in time for the Round of 32 first leg against the Italians.
"The last two days, he (Michu) has reacted well," Monk told a press conference. "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."
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