He has been linked with a number of clubs in the Premier League and abroad, but former Sunderland striker Phillips has claimed that the 33-year-old defender would be a good signing for new United manager Louis van Gaal.
"When he was called upon [by Chelsea] towards the end of the season, particularly in the two games against Atletico Madrid, he was outstanding. He's been the best left-back in the Premier League," Phillips told Sky Sports News.
"Manchester United is getting mentioned already with Louis van Gaal coming in. Will he make a sneaky offer to him? Cole could walk into any Premier League team and don't be surprised if he was to end up at Manchester United. He's got another two or three greats seasons and Van Gaal has only signed a three-year contract. Van Gaal is promising all sorts and there is no better player than Cole to fit straight in there."
Prior to Chelsea, Cole featured on over 200 occasions for Arsenal.