The 29-year-old Spaniard has endured a torrid season-long loan at Napoli, making just five goalless appearances all season, having been a revelation two seasons prior with 22 goals in all competitions for the Swans.
He struggled for injury and form last term and fancied the challenge under Rafa Benitez in Serie A but his future is now uncertain as he prepares to return to his parent club.
Monk said: “Michu is still a Swansea City player and we have obviously monitored his progress there and how he???s got on.
???What I’ve tried to do with that situation is just allow him to concentrate on his football where he is. That was the decision that both of us took in the summer.
???I’ll sit down with him as soon as the season finishes and I’ll speak to him then about his future, and how best to go about it for himself and the future of the club.?????????????????????????????????
Monk will have some serious work to do in terms of recruitment with his strikers this summer.
On loan Nelson Oliveira is likely to have played his last game for Swansea having picked up an injury that will keep him out until the end of the season, before he is set to return to Benfica.
The Welsh club also lost Wilfried Bony to Manchester City in January and Bafetimbi Gomis was reported to desire a move away in the winter transfer window.
The Swans face Arsenal, live on Sky Sports 1HD from 7pm on Monday Night Football, and ahead of the clash at the Emirates, Monk said: ???It looks unlikely that Oliveira will be fit for any of the remaining three games.
???It’s a disappointment for us. Nelson was waiting for his chance and done well in the minutes that he???s played. Then, obviously, in the games he has started recently he has started to do well so that is a big loss for him and for us.
???Bafetimbi Gomis returns. He was in training this week so that’s a big boost for everyone around. So that’s the only changes for the squad.”