The former Atletico Madrid prodigy is out of contract at the end of the season, though United retain the option to extend his current deal by a further year.
Talks over a new long-term deal have been ongoing for some time now, with United boss Jose Mourinho admitting on Friday that he was "not confident" the 27-year-old would pen fresh terms.
De Gea hit back on Saturday, insisting his focus was on winning football matches and not off-field matters and speaking on 'The Debate', Strachan sided with the goalkeeper.
"He deserves the right to choose where he goes and he'll have a few clubs after him," the former Middlesbrough, Southampton and Coventry manager insisted. "But he deserves it after a sticky start where young players can crumble going to Manchester United, we've seen it before - they crumble, they disappear and we don't see them again.
"He dealt with it, physically got better but mentally got stronger. Over the last couple of years, I'm sure he's had approaches and he's dealt with it in the right way. OK, it takes you a little while to get over a knock-back if you really want to go to Barcelona or Real Madrid or wherever it is, but he's dealt with it, he's got on with it.
"He's been a great team-mate and a great servant for the club, so I think it's right that he decides where he wants to go."
A disappointing start to the season sees United sitting 10th ahead of the visit of Everton on Sunday and Strachan believes that United's failure to compete this term could be a major factor in convincing de Gea his future lies elsewhere.
"I think the problem United are having just now is because they are not up there with the top clubs in Europe," he explained.
"They are one of the top clubs, but not one of the top teams at the moment - he'll go back to the Spanish squad and he's got the guys from Real Madrid in the Champions League final, Barcelona, they are winning leagues. He's not winning leagues anymore.
"And I think he's way past the stage of worrying about money. I think what you need now is job satisfaction and as a goalie he's got another 10 years in it. I think he wants to go and be in the top games, the Champions League, cup finals, winning leagues. That's what he's after.
"He may stay but I think sometimes as a player you just want to go and try something different, meet new people.
"I think that's where you start talking to the lad. When you get close to a lad and he decides to move on then you realise there's no changing his mind, that's when you say, "Let's help him."
"Let's help him get the best move and then hopefully he's in fine form when he moves on because I think he deserves that kind of group thing where they say 'thanks very much' instead of making a hassle out of this. If he's made up his mind, then let him go."