The 36-year-old midfielder, whose five-year contract at Los Angeles Galaxy is about to expire, said he wanted to continue playing and was open-minded about what team he joined next.
"When I was [on loan] at AC Milan I played against Manchester United. I'd not played there for seven years and it was special going back but it would be totally different going back there in a Premier League shirt," Beckham told Talksport radio.
"It's a club I love and adore," added the former England captain two days after helping the Galaxy lift the Major League Soccer (MLS) title.
"When I joined United I wanted to start and finish my career there but unfortunately that didn't happen. I could never see myself playing against United for another Premier League team but you never know... stranger things have happened."
Beckham has previously trained with Arsenal and Tottenham Hotspur to keep fit during the MLS off-season and there were moves for him to sign for Spurs on loan in January which narrowly failed to materialise.
He has since been linked with a transfer to Spurs and promoted Queens Park Rangers, as well as Ligue 1 side Paris Saint-Germain.
When asked about a move to France, Beckham said: "Whenever a big club comes in for you it's a temptation. At 36, to still have a big European club after me means a lot.
"I've looked after myself and still feel fresh and that I can play at the top level.
"At the moment I'm still a Galaxy player and I said I'd finish this season, respect the contract I signed, which I've always done, and then sit down with my family and see how I feel and what's going to be best.
"None of the players at Galaxy want me to leave and, if I do leave, it will be sad. I've spent five years in the same team with the majority of these players and I've got to know them so well. It would be sad but we'll see," Beckham added.
"I still love playing and want to play."
He also reiterated he would "love to play for the Great Britain team" at next year's London Olympics.
"Being involved in the bid team that got the Olympics to London was really incredible," said Beckham.
"For me, being from the East End of London, my grandad played football down there at Hackney Marshes, my dad played there, I did too, and to see what is going on there is great. To be part of the GB team would be a dream for me."
