Rice has played every minute of England’s Euro 2024 campaign to date and will be integral to Gareth Southgate’s side for Saturday’s quarter-final clash against Switzerland.
While Rice has been a mainstay in Germany, he has started alongside three different midfield partners across the four games.
Trent Alexander-Arnold got the nod in the first two fixtures but Gallagher came in against Slovenia before Kobbie Mainoo replaced him for the last-16 victory over Slovakia.
Gallagher, who played in the same Chelsea youth side as Rice, reckons the £105million Arsenal man is already among the best in the world in his position, and is not even the finished article yet.
“I can’t think off the top of my head now but he is definitely up there and the exciting thing is he’s getting better as well.
“He’s only just moved to a top team like Arsenal and he’s still improved massively from when he was at West Ham. So it’s really exciting for everyone England and like I said, he’s a top guy as well.
“I think he is pretty much a world-class midfielder, he’s been fantastic for Arsenal so far and I’m sure he’s going to keep improving.”
Gallagher came on to replace Alexander-Arnold against both Serbia and Denmark but a poor 45 minutes when he was handed a start against Slovenia saw the 24-year-old replaced at the interval.
“Obviously it’s not nice,” Gallagher told talkSPORT about coming off at half-time.
“You want to play as much as possible and to get an opportunity to start a game for England at a major tournament is incredible. I was really excited. But it was a really difficult game, I don’t think we were particularly playing great or creating many chances.
“I understand the manager wanted to change a couple of things tactically and bringing on Kobbie to come a bit deeper and get on the ball, progress the ball is completely understandable.
“What is great about the manager is that he came and told me before, before he told the team, so I knew and it was fine. Obviously, you want to play as much as possible but I completely understand.”
Gallagher faces a battle if he is to get back into Southgate’s side but it would not be the first time he has overcome the odds.
He recovered from knee issue Osgood-Schlatter Disease, which occurs during body growth, before then having to undergo minor surgery for an irregular heartbeat – all before making his senior debut.
If he does get onto the pitch in Dusseldorf on Saturday he will, in all likelihood, find himself coming up against Granit Xhaka – the former Arsenal midfielder who has been in fine form since moving to the Bundesliga with Bayer Leverkusen last summer.
“He’s obviously a top player as well,” Gallagher told BBC Radio 5Live.
“He had a good time at Arsenal and obviously had a fantastic season at Bayer Leverkusen.
“Obviously he’s got loads of experience, a lot of quality. He’s a leader for Switzerland. So we’ve got to make sure we’re at our best whoever comes directly up against him, he is a great player.”
