AS Monaco officials are expected to arrive in Los Angeles in the next 48 hours for preliminary discussions with David Beckham's representatives.
The 37-year-old is understood to be open to a move, having announced his desire to leave Los Angeles Galaxy following Saturday's MLS Cup final.
Beckham has attracted interest from clubs in Brazil and Russia, but Monaco appear to be leading the chase.
Talks are expected to start after LA Galaxy take on Houston Dynamo.
Monaco chief executive officer Tor-Kristian Karlsen told BBC Sport "We are happy with our current squad.
"But if there's a chance to get a player of Beckham's stature, we'd be foolish not to explore it."
Earlier, former England captain Beckham, who has also been linked with Queens Park Rangers, West Ham and Paris Saint-Germain, said he was unaware of interest from Monaco.
"I heard the Monaco thing on the way to training this morning from a friend in London who said: 'I hear you are going to Monaco?'," he said.
"That was the first I had heard of that. I am very flattered by some of the serious interest I have had.
"It is always nice to be recognised by good managers with Carlo Ancelotti, Harry Redknapp and Sam Allardyce saying they would love me to play, it means a lot to me."
Beckham plans to make a final decision on his future by the turn of the year.
Karlsen added: "Right now we're trying to learn if Beckham's future ambitions are in sync with ours.
"I understand he's high in demand but it's natural for a player with his experience and quality. Let's see what the next few weeks bring.
"It's a privilege to be linked with world-renowned players like Beckham."
Beckham is due to play for LA Galaxy in Saturday's rematch of last year's MLS Cup final. LA Galaxy won that game 1-0 to earn Beckham his first piece of silverware in the United States.
But Monaco, who play in the second tier of French football, Ligue 2, following their relegation from Ligue 1 in 2011, look set to begin talks with the midfielder after he announced he was to leave the Galaxy for "one last challenge" before retirement.
Billionaire Russian businessman Dmitry Rybolovlev bought a majority stake in the club in December 2011, with ambitions to return them to the level they were once at.
Monaco boast a fine history, with seven French league titles to their name and alumni such as George Weah, Yaya Toure and Englishman Glenn Hoddle.
They were also managed by Arsene Wenger between 1987 and 1994, the now-Arsenal boss winning the title in his first season at the club.