The ex-Gunners star says Wilshere should not go to France unless he can prove he is 100% fit.
Due to injury, Wilshere has not played a single competitive minute of football for club or country since scoring twice for England against Slovenia in June.
Three Lions manager Roy Hodgson, under whom the 24-year-old has been a regular for his country when fit, last week offered the midfielder hope of a place in his squad if he returns before the end of the season.
However, Parlour is adamant that if there is even the slightest question over the player's fitness when the time comes to name his squad, Hodgson should not select the Arsenal man over a fully fit option.
The 43-year-old told talkSPORT: "I wouldn’t take anyone unless they’re 100 per cent fit. I don’t think you can take that gamble. There’ll be no rushing back for Jack. Arsenal are taking their time with him, they’re going to get him exactly how they want him before he plays again.
"But if he can get back into the squad and play six games before the end of the season, starts playing on a regular basis and starts showing his form again…Roy has always been a loyal man, and he’ll be loyal to the players who have got England to the Euros.
"I think Jack Wilshere will go if he IS fit, but there’s a lot of competition for places. Roy’s got a real dilemma with who he picks, especially in that midfield area."
Wilshere has won 28 caps for England since his international debut six years ago, a total that would surely have been far higher had he not been plagued by persistent injury problems throughout his professional career.
He is certain to miss the Three Lions' friendlies against Germany and the Netherlands at the end of March, but will be desperate to prove his fitness in time for the Euro 2016 squad announcement in May.