The Los Angeles Galaxy star's five-year stay with the Major League Soccer outfit comes to an end at the weekend sparking speculation about the 37-year-old's future.
Monaco are in the second tier of French football but have big ambitions following a takeover by Russian businessman Dmitry Rybolovlev and the location could be attractive to Beckham.
"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," Karlsen said.
"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 has since played down the reports of a move to the principality but stopped short of ruling out a deal.
"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 the former England captain.
He added: "I've got some interesting and exciting options on the table."