Kewell opted to join Liverpool from Leeds United in 2003, but Scholes says Manchester United was also an option at the time.
Scholes was asked if there were any players he was excited about playing with after rumours emerged they were about to be signed by Sir Alex Ferguson, but the move ended up falling through.
"I always remember two or three who were possibly coming, I remember Harry Kewell was one and you knew what a good player he was,” Scholes said on Savage Social.
“He was brilliant. I think he ended up turning us down and going to Liverpool which didn’t really bother us that much.
“I think Damien Duff at the time was another one. Arjen Robben, I think he was very close to coming.
“As a midfield player you look forward to playing with quick players who can run with the ball and score you goals.
“But I think the one that stands out is Ronaldinho. I really thought the manager got him.”
"I think we were away for pre-season, it was as close as announcing him and giving him a number.
"But I think he ended up changing his mind at the last minute and signing for Barcelona. It’s strange really because on that pre-season tour we were playing against Barcelona."