Beckham will be 38 in May, and while he has not made a decision yet as to whether to play on, he revealed he was "honoured" that manager Carlo Ancelotti and the club's owners want him to continue.
"The owners and the manager have made it very clear that they would like me to stay here. I'm very touched and very honoured," Beckham told Sky Sports News, after being announced on Thursday as an ambassador for the subscription broadcaster.
"I'm enjoying this season so far, I'm going to enjoy it until the end of the season. Hopefully we'll be successful then we'll make the decision on what I do.
"To be honest, I'm 38 in May and you get a reminder of your age every now and again, but I'm still enjoying playing. I love playing and until that goes away I hope I can continue."
The former England captain and Manchester United favourite added: "It's something that I'm not even really thinking about right now and until I decide that's the right thing to do, retiring is not an option yet."