The midfielder is out of contract at Pittodrie at the end of the campaign and is closing in on a move to Ibrox as Pedro Caixinha looks to kick-start his Light Blues rebuilding job.
Boss Caixinha spoke of his admiration for Jack earlier this week and now looks set to land one of his main transfer targets.
He said: "Ryan had a big injury a couple of years back and was out for a while, but I have seen him three or four times with Aberdeen at any different stadiums and they have always performed and he's one of the players you would say is a good player.
“He's recovered well from a bad injury and he is a young player playing with confidence in a confident side with good players. He definitely stands out for Aberdeen. He creates too and that's why Aberdeen are where they are.
“If you are a good player and you can make that step, then the supporters appreciate good players. That's the end of it. If you can come here and play well then it doesn't matter who you played with.
“If you are a good player and you can come and play in this environment week on week then the fans will take to you.”