The Spaniard, who has six goals in all competitions this season, missed Sunday's 4-3 Premier League defeat at Liverpool with an ankle injury.
But Monk is eager to keep hold of a player who struck 22 times last season as the Welsh club finished in the top half and won the League Cup.
On the link to Anzhi, Monk said: "I heard it today (Sunday) and it's one of them. Obviously Michu's the type of player who is going to attract interest, he's a good player.
"He needs to get himself fit, that's got to be his first priority. The bottom line is we're not a selling club, we don't just sell our players, and those that have moved on are ones where it's been done at the right price.
"I'm not saying that we'd ever sell Michu, I just said we're not a selling club. We'll just treat that as speculation, there's been no offer or anything like that. He's part of our plans and part of what we want going forward.
"I've spoken to him a number of times since taking over and there's nobody more eager to get out there on the pitch than him. Hopefully he's back in training next week."
Swansea showed commendable spirit at Anfield to battle back from behind twice before Jordan Henderson's late goal wrapped up the points for title-chasing Liverpool.
Wilfried Bony scored twice, including a penalty, with Jonjo Shelvey netting a stunning strike against his former club.
Monk was less than impressed with the first-half showing but was happy with their renewed vigour after the interval.
"First half I wasn't happy, we were a bit too slow with the ball," he said. "We weren't passing it quick enough, but I think once we sorted that out, second half we were back to ourselves, believing in what we were doing, moving the ball quicker, and we got the goal which was great.
"We've come here to a side pushing for the title and to give them such a good game and be in it to the very end shows you how well we've done."
