Hammers co-chairman David Gold is a long-time admirer of the former England captain and even tried to sign the 37-year-old back in 2010.
And, with Beckham set to end his spell in the MLS in December, former Upton Park favourite Martin claims the former Manchester United star can help Carroll, who is yet to score for the club since making his loan move from Liverpool, end his goal drought.
“He should go to West Ham,” Martin said. “If West Ham are doing as well towards the end of the season as they are now, then why not?
“He’d be perfect at delivering balls for Andy Carroll. He’s still got another year or two in him yet because he’s not all about pace or athleticism.”