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The 48-year-old ex-Manchester United skipper shared a legendary rivalry with Vieira when the Frenchman played for Arsenal.
And when he was asked to name his toughest opponents, Keane admitted that he had to be at his "very, very best" when he crossed paths with Vieira.
Keane told Sky Sports' Monday Night Football: "It was a big challenge for me when Patrick [Vieira] came onto the scene.
"He was a good player and I knew I had to be at my best when I was up against him. He was nasty, he could put his foot in and he could score a goal.
"Patrick would've been my toughest opponent at the time. He would challenge you in different ways.
"He would get around the pitch, he was good with the ball, he was strong and he had a goal in him. I knew I had to be at my very, very best to get on top of Patrick."
Keane went on to talk about the Premiership and picked out Rob Lee, Gary Speed and David Batty as formidable opponents he came across.
The Red Devils legend continued: "He [Vieira] wasn't the only one, though.
"Back in those days, every week in the Premiership you were in for a battle: David Batty was tough; Gary Speed, God rest his soul, he was tough; Rob Lee up at Newcastle -- you knew you were in a game against these fellas."
Keane, who retired from football in 2006, won the Champions League with United in the club's historic treble-winning season.
And the former Nottingham Forest man came up against strong opposition during his matches in Europe.
According to Keane, Zidane is the one player who "had everything" and was "nasty with it, too."
He explained: "The greatest I faced in Europe? Undoubtedly Zidane. He had everything -- but he was nasty with it, too.
"Batty, Speed, they were nasty, too, they'd give you a kick, a real battle; I just gave back as good as I got!
"But there was a respect towards Patrick. It was the same with the lads coming through.
"I go back to Steven Gerrard and Frank Lampard. You had to be at your best. I had huge respect for him, but I knew if I could win my battle, it would give us a better chance of winning the game."
Featured Image Credit: PA
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