Beckham's contract with Major League Soccer's Los Angeles Galaxy expires next month, and he will be free to join any club from January.
The Galaxy have made a concerted move to try and convince the 36-year-old to stay in California, but he also has offers to return to Europe.
In England the likes of Tottenham, QPR and Leicester are all keen - but big spending Paris Saint-Germain have emerged as favourites for his signature.
Beckham admits he is now considering his options, refusing to rule anything out, or anything in.
"I have had a lot of offers and I must say that I'm amazed that, at my age, I have had so many. It's been a bit of a surprise," he told the Daily Telegraph.
"I have to see how my body feels once the play-offs are over, but I love it here and there is a real chance I will stay, especially if my family are happy."
But Beckham did admit there was interest from PSG and that playing in next summer's Olympics was still top of his list of priorities.
"What will actually happen next I still can't say, but what is very important in the decision in terms of what I do, be it staying here, or going to PSG or wherever, is that I get enough time on the pitch because I want to be part of the Olympics," he continued.
"I've made no secret of that. Even to be in the team would be incredible. To be part of that Olympic spirit and to be able to win gold for Britain would be the ultimate [goal] for me.
"The fact that we've got the Olympics in the east end of London where I grew up, the fact that I could be part of that and that I could be out there trying to win gold would mean a hell of a lot to me because I am very patriotic.
"So whoever I sign for, to make sure I would be ready to make that attempt, I would have to be playing regularly."