Pirlo - who will retire from international football at the end of this summer's World Cup - is one of the key men in the Italy side that England will face in their opener in Menaus on Saturday night.
His performance in the Euro 2012 quarter-final was highlighted as one of the main reasons England failed to progress, as they went out on penalties, with the Juventus midfielder putting in a commanding performance in Kiev that night.
Despite that display, Parlour told TalkSport there is no need for England to man-mark the midfielder.
He said: “We should not be man-marking Pirlo. Pirlo has been a fantastic player for Italy but he’s getting on a bit now.
“He’s still got that [brilliant] passing ability and he will try and control games. Steven Gerrard is just as good, though, if not better than Pirlo.
“I don’t think England should be worried about players like that.”
Gerrard had a terrific second half to the season for his club in the deeper midfield role as Liverpool finished second in the Premier League and certainly has the qualities which are effective in a deeper position.
His range of passing and reading of the game is up there with the best, as is Pirlo's, and some will view their performances as one of the key battles when they face each other on Saturday.
It has been suggested that if England give Pirlo special treatment and mark him out of the game - former Manchester United midfielder Paul Scholes mentioned this as a possible strategy - then they can get the upper hand in midfield and dictate the play, rather than giving him time on ball and allowing him to take charge of proceedings.
Either way, it is likely that the performances of both men could have a big say on the result of their Group D opener this weekend.