Cole has been with the MLS side since the start of 2016 but with just a few months remaining on his current deal, Birmingham are looking to pounce.
According to The Sun, Blues boss Harry Redknapp has identified the left-back as one of his top transfer targets this summer as he looks to build a squad capable of challenging for promotion.
The West Midlands outfit only avoided relegation to League One on the final day of the last campaign, but Redknapp has already brought in the likes of David Stockdale, Marc Roberts, Craig Gardner and Cheikh Ndoye.
Cole has impressed during his time in California and it has been claimed that the club are looking to extend his time in the United States.
The 36-year-old has not featured in English football since he ended his time with Chelsea in 2014.