The Italian giants welcome the reigning English champions to the San Siro on Tuesday for the first leg of the eagerly anticipated clash and Cole thinks his former team-mate should not expect a straightforward evening.
"It is going to be very difficult for Becks," said Cole, according to Press Association Sport.
"Manchester United were the club he always wanted to play for; the club he won so much at and served with such distinction.
"The fans love him and he has a special place in the club's history.
"He has nothing to prove but it is the first time, and there will be so much going through his mind. It is bound to be hard."
Cole also thinks brushing off Milan as an aging team would be a dangerous thing for United to do.
Experience can be just as dangerous a part of team's make-up as youthful enthusiasm according to the man who won the Champions League in 1999 alongside Beckham.
"Age is just a word," he asserted.
"They said exactly the same thing when United last went there three years ago and they got beaten 3-0.
"Once you get out onto that pitch, it doesn't matter how old you are, and that goes for David Beckham, Paul Scholes and all the other players who are labeled in that bracket.
"You become better by playing with a higher standard of player and the later you get into your career, the more determined you are to stick around with all the other quality players."
"People say Becks' legs have gone but his positional sense is probably better than it has ever been and there are enough younger ones around to do some of the running for him."Keep up to date with all the latest Champions League news with Goal.com