The ex-England international is due to see his contract with the MLS club expire later this year, leaving him available to join the Blues for a minimal fee if an agreement can be struck.
Birmingham were linked with the 36-year-old earlier this week and Redknapp has now hinted that he could make an approach, claiming that Cole still has plenty left in the tank to help with City's Championship promotion push.
"Ashley Cole is still in great nick," he told reporters. "Someone mentioned him and I thought 'That is an interesting player, for sure'. You can't beat a bit of quality.
"And for me he was possibly the best left-back in the world a few years ago at one time when he was at Chelsea. I know Ashley, he's a great lad and he could certainly play at this level - no problem."
Cole has spent the last 18 months at Galaxy after bringing an end to his time in Europe, seeing him take in spells with Arsenal, Chelsea and Roma.