The 29-year-old France international was a target for Dubai-based club Al Ahli, but they have now ended their interest, according to reports.
Al Ahli believed they would be able to take advantage of certain clauses in Gomis’ contract at the Liberty Stadium, but it is understood those clauses are not what they thought.
Monk had already said he was keen to keep Gomis, who finished last season strongly with six goals in his final 10 league games, and he repeated his stance following Friday’s 1-1 friendly draw at Reading.
Monk told Sky Sports News HQ: “He’s a Swansea City player and we are looking forward to working with Bafe for this season.
“He’s come back in really good shape and is working very well so we are looking forward to the season coming up.
“There is always speculation and obviously I think there was contact from that club to our club but that’s as far as it goes and, like I said, Bafe is looking forward to a season with Swansea City.”
Spanish forward Michu remains a Swansea player for the time being, but he is not in Monk’s plans and the Swans boss expects him to depart in the near future, with a return to Rayo Vallecano one possibility.
Monk said: “He’s trying to sort out, and the club are trying to sort out, an agreement where we can find him a club to move to, but that agreement has to be right for all parties.
“Hopefully we can resolve that situation as soon as possible.”