Cole, 35, left Roma on Tuesday after his contract was terminated by mutual consent, having failed to make a competitive appearance for the Serie A club since last March.
He is now widely reported to be joining the Galaxy on a non-Designated Player deal [h/t LA Times], and Gerrard believes the former Arsenal and Chelsea left-back would prove a great addition to the club.
"I'd be delighted if Ashley Cole becomes a teammate at the Galaxy," the Liverpool legend told ESPN FC. "[He's a] world-class player. I think he's still got a couple of years to offer. Defensively as a team we made big mistakes.
“We weren’t good enough defensively last year as a unit, and I think Ashley will help us improve."
Nevertheless, Cole may not be a popular signing with most Galaxy fans to begin with at least, having come in for criticism for his comments about MLS upon joining Roma on a free transfer in the summer of 2014.
The two-time Premier League winner acknowledged that he had received offers from several American clubs after leaving Chelsea at the end of the 2013-14 season but told reporters that he “didn't want to sit on the beach yet”, before later taking to Twitter to further belittle the standard of the league.
His opinion may well have changed over the following 18 months, but he will likely face questions about his commitment once his anticipated move to LA is confirmed.