Tate came through the system at United before moving on.
"It'll be nice to see my old friend Alan Tate who I played with in the youth team," Fletcher recalled to manutd.com. "He was a couple of years older than me and always looked after me and made sure I was okay when I first came to Manchester.
"I'll always remember him for that. He's recovering from a bad injury at the moment and the sooner he gets back in the team the better it'll be for Swansea because he's a top player.