Beckham was linked with a move to the fallen giants by the British press, but he said no talks had taken place, hinting he would rather play for a top-flight club.
"I heard about Monaco on the way to training this morning from a friend in London who said 'I hear you are going to Monaco.' That was the first I'd heard of that," said Beckham at an LA Galaxy press conference ahead of his last match for the club, the MLS Cup final against Houston.
Beckham has revealed he has numerous offers to continue playing when his Los Angeles Galaxy career ends this weekend, but the former England captain is reportedly set to open talks with the French Ligue 2 side after Saturday's MLS Cup final against Houston.
The 37-year-old is ready to bring the curtain down on six seasons in Major League Soccer with several clubs lining up to sign the former Manchester United and Real Madrid star.
Monaco are owned by billionaire Russian businessman Dmitry Rybolovlev, who bought a majority stake in the club a year ago.
Beckham has helped raise the game's profile in North America since joining the Galaxy in 2007.
"I've got some interesting and exciting options on the table," he told a news conference.
"I am very flattered by some of the options that I've got. I still feel I can play and I'm not considering retiring."
The 37-year-old former Manchester United midfielder has been linked with a number of clubs internationally, with the latest being French team Monaco.
But Beckham outright dismissed speculation linking him with the recently reformed New York Cosmos club which will play in the US second tier next season.
"I've been hearing the Cosmos thing for the last two or three years. It's not true. My manager has definitely not had conversations with them, that's definitely not true," he said.
Beckham did say, however, that he has received some serious approaches and singled out three managers, who have talked positively of him recently, for particular thanks.
"I've still got managers like (Paris St. Germain coach) Carlo Ancelotti and (Queens Park Rangers manager) Harry Redknapp and (West Ham United manager) Sam Allardyce ... coming out that are saying they'd love me to play and they know how professional I am, it means a lot to me," said Beckham.
"It is what I have tried to base my career around, over the years, being professional and working hard, so it's nice to be recognised like that."Beckham, who moved to the US after winning the Spanish league title with Real Madrid, also spoke positively of his six years in MLS, each spent with the Galaxy, but despite the 'end of an era' mood he dismissed the thought of now being an opportune moment to retire from the game.
"I do believe I still have got another challenge inside, that I can still play for, I don't know how many years left. I do still feel I can play," he said.
Beckham will end his playing time at LA, where he has also been linked with a possible off-the-field role, with plaudits from MLS officials and fans.
But he acknowledged that his six seasons with the Galaxy had included some rough times, particularly in 2009, when local fans reacted with anger to his decision to go to Italian club AC Milan on loan during the first half of the MLS season.
"Go Home Fraud" read one bluntly worded banner draped over a section of the Galaxy's Home Depot Center at the time.
"I've never been booed by my own fans with other clubs, but I've had that at certain points here, and I overcame that," he said.
"It's never a happy moment to be booed by your own fans and seeing some of the banners that were out there.
"At the end of the day, I was happy that I turned it around, and I think now the majority of fans are on my side."
Winning the title last year certainly repaired that relationship and he is certain to be given an emotional send off by the Galaxy fans on Saturday.
But Beckham's role in MLS however has always been as much, if not more, about promoting the league to a traditionally football-sceptical public, and he believes the status of MLS has risen during his time in the States.
"The interest now, when this league is talked about in Europe, people are starting to take it very seriously and that is an amazing thing to see," he said.
Beckham has a contractual option to take an ownership role in a future expansion franchise and there has been talk of a possible ownership role at the Galaxy in the future.
But regardless of what his precise role will be, Beckham says that he will remain involved in supporting the growth of MLS.
"Just because I'm not playing here anymore after the weekend, my commitment stays the same and I will do anything to keep these players coming over like Robbie Keane, like Thierry Henry," he said.
"Anything I can do on that side of things, I want to do. I want to see this league continue to grow."