Monk: Michu closing in on Swansea return
The Spain international has only made 12 league appearances this season, scoring twice, and he has yet to feature under Monk.
Monk replaced Michael Laudrup last month but has had to cope without last season's top scorer, however he is optimistic on his chances of returning soon.
The 27-year-old underwent surgery on an ankle injury in December but is due to return for the final 10 games of the campaign.
"I would say at this stage that Michu has a chance," Monk told The South Wales Evening Post.
"He trained both days over the weekend and then had a rest on Monday, but he will be working from now on.
"And if he trains well over the next few days, he has definitely got a chance of being involved.
"He won't be starting I wouldn't have thought, but you never know.
"We will have to see how he is in training. In this situation, a lot of it comes down to how the player feel as well. He said the pain he has been feeling has gone now, but we have to make sure we don't rush him.
"I will speak to Michu over the next few days and we will go from there."