The Royals face the Premier League club in the third round at Old Trafford on Saturday having faced them twice in the competition in the last 10 years
Stam made 79 appearances in all competitions for the Red Devils between 1998 and 2001, which included winning the FA Cup in his first season, but he left in controversial circumstances.
The Dutchman recalled in his autobiography that Sir Alex Ferguson, then United's manager, met him at a petrol station, got in his car and told him he had to be transferred.
It was suggested at the time that Stam's exit was inevitable after comments he made in an earlier book
Ferguson and the club strongly denied that at the time, insisting it was purely a football decision to sell him to Lazio, but the Scot did admit in 2013 it had been a mistake to let Stam go.
Speaking about facing United, Stam said: "Hopefully (the Manchester United fans) support me on Saturday - I've heard they still sing my song
"It tells you something in how I performed when I was there and the relationship I had with the fans.
"I've never been back in a proper game - I've been back for the games we played for Soccer Aid - but it'll be good to be back in front of the United fans in a situation like this.
"But it's not an opportunity to say a proper goodbye to them, because hopefully I'll be back again as a manager coming up against them in the future."
Even aside from the United connection, Stam sees it as a chance for his Premier League hopefuls to go up against one of the country's top clubs.
"It's always nice for a manager and his team to play against teams like Manchester United to see what you can do, what you are capable of," he said
"Then you can see where you can improve as a player and how the team can be better going into the second half of the season."
Reading have not beaten United since 1927 in all competitions but Stam believes his side are more than a match despite coming up against Jose Mourinho
He said: "He's the type of manager who wants to win the league, the Champions League, the FA Cup, everything! That's what I like about him.
"He's up there, I'm down here
I still need to learn a lot, I need to improve myself as a manager
I can learn a lot from him in how he works
He's a great manager.
"Everyone always looks forward to games like these
We want to show ourselves at Old Trafford against a side like Manchester United.
"We know they are in form and it doesn't matter which players they play - they have so much quality
So we know it's going to be difficult.
"But we've got confidence as well
We believe in ourselves
We believe we can do something
But that doesn't make it any easier when you're up against a team like United
"You need to enjoy it but you'll enjoy it even more if you get a result.
"The thing is if you go into these games, you enjoy them and you play against a very good side, but it doesn't mean if you play a side like that at Old Trafford you're going to lose straight away.
"You need to give it your best shot, work very hard and be confident in how you play
And then I'm sure we can do well against them.
"They will probably want to finish the game as quickly as they can, so we need to be prepared."
Source : PA