The Welsh club announced on Wednesday that the Ivory Coast international had put pen to paper on a deal to prolong his stay at the Liberty Stadium until 2018.
Bony had previously been linked with a move to the likes of Liverpool and Arsenal, but Monk does not believe the rumours will stop.
"It's not our problem," he said. "Our problem is to try and sign and keep players on long-term contracts for as long as possible.
"Bony is one of them. We can't stop speculation whether they're on a one-year or 20-year contract.
"My priority is that players are happy and are rewarded.
"I don't delve into the details. I give my advice whether players deserve it or not and leave to the chairman to discuss the details with the agent.
"We're happy to have him [Bony] and he's happy to be here, which is the main thing."
Bony came on as a half-time substitute as Ivory Coast drew 0-0 with Cameroon to book their place in the Africa Cup of Nations on Wednesday and Monk has mixed feelings about the result, which will see him lose his star striker during the tournament.
"It's bittersweet," he added. "I'm happy for him, he's playing for his country to qualify for major tournaments, but it's disappointing to lose him for a period.
"We wish him well but we have other players who can step in."
