"When I was at Arsenal, Manchester was the best team in the country, because they were winning the League in the last four or five years," Vieira told The Sun.
"There was a big rivalry between the two clubs and every single game that I played against Manchester has been tough, has been difficult.
"There was a lot of tension, a lot of arguments, battles. But it was fantastic. I loved it a lot.
"Of course, talking about tension, there was some on the pitch, some outside the pitch and that makes me laugh now."
Vieira's lowest point was receiving a red card at Old Trafford in September 2003 after a spat with United striker Ruud van Nistelrooy. The arguments and scuffles between players continued at the final whistle and later in the players' tunnel.
"We played at Manchester and I was sent off during the game because I made a tackle and Van Nistelrooy acted like he was making a movie," said Vieira.
"I got really frustrated about it and wasn't happy at all.
"After the game, I saw him next to the coach and we exchanged a few words. That was quite funny."