Monk could be without leading Ivorian marksman Bony for up to six matches once the showpiece African tournament - to be held in Equatorial Guinea - gets underway in the New Year.
Bony's absence has led to speculation that Michu - on loan at Serie A outfit Napoli - could return to Wales to fill the void.
But Monk was quick to dismiss the Spaniard's possible return when quizzed by reporters, instead claiming he could delve into the transfer market.
"Michu is on loan at Napoli for the season," Monk said. "I'm not even thinking about that, I've not even checked the details of the loan.
"Obviously Ivory Coast's qualification dictates what you do in terms of January. We may have to go into the loan market or do something to cover it.
"We've already been looking at all the positions but now Bony has qualified a striker is the position we do now have to cover.
"We could promote from within, but it is likely to be a loan. It might be a loan with a view to a permanent or to next season, or just for a month."
Swansea travel to defending Premier League champions Manchester City on Saturday.
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