May played with Beckham for nine seasons between 1994 and 2003 for United, and admitted he was surprised that the former England captain announced his retirement on Thursday, after recently winning Ligue 1 with PSG.
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"I am a little bit shocked to be fair," May exclusively told Perform. "When I first heard it, I was surprised because he has done so well at PSG this year, I thought he would carry on.
"As a person he is very down to earth and family orientated. His dad still comes to Old Trafford as often as he can and I sure Becks will come more, I am sure of that.
"As a lad he was very down to earth and you knew where you stand with him. He was one of the lads and he came through in the 94-95 season when the kids would win nothing.
"I think he is a United fan, you see a lot of the ex-players coming back and obviously with his time in America and Paris he was limited when he could come here but now he can come back and bring the kids and enjoy Old Trafford as a fan not a player.
"It is quite an achievement, he has managed to win six Premier Leagues, two FA Cups, a European Cup and he won La Liga, and has gone over France and managed to win that and also in America so for him to do that in a career spanning 700 games is a remarkable achievement.
"I think his legacy will be as a fantastic footballer, a great ambassador and a great lad to be around. People might see him in a different light from what I see him in but he was great to be around, fantastic character and a good laugh."