The 36-year-old is reportedly keen to return to England for the first time since leaving Manchester United in 2003.
Amit Bhatia confirmed that Rangers were interested in bringing the midfielder in on loan.
"Would we like to have him? Most certainly," said Bhatia.
"I am just not sure it's a real possibility. We would like to sign people of Beckham's calibre. I am just not certain Beckham would choose to come to us as a newly-promoted side.
"If he came to London, maybe he'd choose a bigger club like Spurs."
Since joining LA Galaxy in 2007 Beckham has had January loan spells with Italian club AC Milan.