Falcao has just one year remaining on his current contract, and with Monaco showing no signs of giving him a long-term contract, the Colombian international is eyeing a move to an alternative destination.
Falcao was back among the goals as Monaco continued their pre-season preparations with a 1-0 win over Sampdoria, and he admitted afterwards he had received offers and was studying them.
"The truth is that I still have a year of contract and the club did not offer me an extension," he said after Saturday's victory.
"So I have to think about my future, my family.
"I am studying the offers I have been offered. These are good opportunities for my career.
"I have to think about my family."
"I still have only one year of contract and it's complicated for a player of my age," he said.
"I think the club understands my position to give my family some peace for the future."
The 33-year-old has been on the books of AS Monaco for the past six seasons, after joining from Atletico Madrid, but he has spent two of those years in England in underwhelming stints with Manchester United and Chelsea.
Falcao has however recaptured some of his old magic in recent years, scoring 15 Ligue 1 goals to help Monaco escape relegation last term.
Among the clubs reportedly interested in Falcao are Galatasaray, Valencia and former club FC Porto.
Monaco begin the 2019/2020 campaign with a home game against Olympique Lyon at the Stade Louis II on Friday.
