The midfielder made his competitive debut for England on Monday as he came on as a substitute in the 2-1 win over Tunisia.
“I was really impressed by Loftus-Cheek when he came on," he told talkSPORT.
“He looked lively and had that ability to go past a player from midfield.
“I just had a funny feeling, and I'm not comparing them by any stretch, but my first World Cup as a kid was Italia 90 and Gascoigne obviously started that tournament as a squad player.
“He had the number 19 on his back and by the end of the tournament he'd really been taken into the country's hearts.
“I just have a feeling that could be Loftus-Cheek for England in Russia.
“He's got that kind of quality, I really think that boy is that good of a player and I'd love to see him start getting more game time."