Falcao has made no secret of his desire to join Galatasaray, with his agent Ahmet Bulut saying earlier this month that he is working on a deal to get his client a move to the Turkish side.
But, at a news conference on Wednesday, the club chief said that the 33-year-old would still have to respect a contract that runs through the end of this season.
"Falcao is a great professional," Petrov said. "He has ambitions obviously, he wants to play the Champions League and we understand him, but we want him to stay at the club, he has a contract and he has to respect it."
Despite Monaco's poor 2018-19 campaign, Falcao still managed to net 15 times in Ligue 1 last season, good for joint-fifth in the league's top scorer rankings.
"I am studying the offers I have been offered. These are good opportunities for my career," the Colombian said.
"I have to think about my family."
Perhaps in preperation for Falcao's exit, Monaco completed the signing of striker Wissam Ben Yedder from Sevilla last week, paying the France international's €40 million (£37.1m/$44.7m) release clause.
With Falcao out of the line-up, Ben Yedder was rushed into the squad on Saturday as Monaco fell 3-0 to newly promoted Metz.
The defeat continued a poor start for Leonardo Jardim's side, who sit bottom of Ligue 1 with two 3-0 defeats in as many games.
Petrov, though, did not want to blame his manager for his side's dismal start to the new campaign.
"We are aware that the start of the season is not up to the ambitions of AS Monaco but I do not think it should be laid on Leonardo Jardim," he added.