Although the former Liverpool captain made it clear that he has “nothing but respect” for the pair now that their respective playing careers have ended, Gerrard spoke of the “hatred” in lining up alongside them in the tunnel before matches.
Gerrard, who made more than 700 appearances for the Reds across 17 successive seasons, will have clashed with the Manchester United pair on numerous occasions as a player, and the ex-England international spoke openly of the rivalry they shared.
"When you're lining up against in the tunnel against Rio and Gary Neville you want to do everything in your power to beat them, there's hatred there, that's exactly how it is,” he said at his first-ever ‘Steven Gerrard Live’ event on Monday night.
"When you meet up for England at that time, you pretend you like them, but your career finishes, their career finishes and your friendship starts for real.
"I've got nothing but respect for Rio as a player, played for a top club all his life, he's a good fella as well, I'm enjoying the role at BT [Sport TV] with him as well."
Gerrard was also asked about his relationship with former Liverpool boss Rafa Benitez at Monday's event.
Describing it as “cold”, the 37-year-old said there were times he thought the Spaniard “just didn’t like him”.
He admitted, though, that it was likely down to Benitez’s style of management which struck a stark contract to the “arm around the shoulder” approach he had been used to under Gerard Houllier.
Gerrard left Liverpool in 2015 to join MLS side LA Galaxy but has since returned to Anfield and now coaches the club’s U18s team.Reuse content