Since their relegation from the top flight in 2010, Monaco have been taken over by billionaire Russian businessman Dmitry Rybolovlev, who has lofty ambitions to restore them as a major force.
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."
He went on: "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."
Sources close to the player have confirmed an approach by Monaco, who are an ambitious club with wealthy owners, but that they are not regarded as favourites.
Beckham would probably prefer to go to Ligue 1 heavyweights Paris St Germain if a suitable offer is forthcoming and team up again with coach Carlo Ancelotti and team director Leonardo, whom he knows from his two previous loan spells with AC Milan.
There are also offers from China, Russia and Brazil on the table which Beckham will consider after the Galaxy's MLS Cup final against Houston.
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