Everton manager David Moyes told reporters ahead of Saturday's match at home to West Bromwich Albion that the 35-year-old, who is a close friend of captain Phil Neville, would be a welcome addition in the January window.
"I would hope that if David wanted to come he would pick up the phone and call me," said Moyes, who is still hoping to re-sign Beckham's Galaxy team-mate Landon Donovan on a second three month loan deal.
"I know him and if David Beckham wanted to come back to the Premier League, he would only need to call me or Phil. We would be here for him at Everton."
The Londoner, who has 115 England caps, was ruled out of his country's World Cup campaign in South Africa this year by an Achilles tendon injury and returned to action for the Galaxy in September.
"If he wants to come back and play under me, and with Phil, he can do that," said Moyes.
"I think he would feel he could do that to a lot of clubs in the Premier League. We would have to look into it financially but if he came and said to me 'I would like to come and play' I would have to go the chairman and ask if we could do it."
