The injured Colombian was absent from Stade Louis II on Sunday as his side secured a 1-0 win over Ajaccio but the former Barcelona man insists he is happy to stay at the club
The Colombian was missing from Claudio Ranieri's squad due to a thigh injury but was not even in the stands at the Stade Louis II stadium to support his team-mates, fuelling speculation that the player could be pushing for an exit from the club as early as January.
Abidal, however, shrugged off any suggestions that the striker's absence spelt the beginning of a transfer saga brewing in the principality, insisting the former Atletico Madrid man is happy to stay at the club.
"One thing is for sure - he is really injured," the former Barcelona left-back told Canal + after the match.
"He said he wasn't going to leave, he would stay. He wanted to come to AS Monaco, he is here now and he is a great professional.
"As I say each time, we do everything to make sure he's in the best condition. The most important thing for him was not to aggravate the injury. It takes time to heal and we'll try to make do while he is not about.
"There were rumours that he was away to get treated. Whether he has to be treated in Monaco or elsewhere, the important thing is that he can return very quickly and 100 per cent fit."
Falcao is expected to return for the trip to Guingamp next weekend.