Eagles spent Wednesday discussing a deal with the SPL champions after Burnley accepted their offer for the former Manchester United youngster.
The 24-year-old, who has 12 months left on his contract at Turf Moor, has gone away to think about the deal and is expected to provide an answer within the next 24 hours.
"He is a good player," said Walter Smith in the Daily Record.
"We watched him at Burnley and if he signs it could be a good help for us, but we will have to wait and see."
Thompson, who used to play for Rangers himself, reckons the Ibrox faithful would enjoy watching Eagles in action.
He said: "I think Chris would be a sensation for Rangers. He's a very talented young man and he'll certainly entertain the fans at Ibrox.
"Rangers supporters have been looking for a player like this for a few years now. It's been a while since they had a born entertainer to watch and that's exactly what Chris is.
"He's got bags of skill, he's quick and he'll pitch in with goals. For £1.5m it would be a great bit of business."
Clarets boss Brian Laws is keen to keep Eagles at Turf Moor, but he will leave the decision up to the player.
He told the club's official website: "I will sit down with Chris this morning and see what is on his mind following yesterday's developments.
"Clearly he is a talented player and one I do not want to sell.
"But we have a serious financial offer on the table and with only 12 months left on his current deal we have to be aware that Chris could walk away next summer for nothing.
"I spoke to him yesterday on his way to Glasgow and he promised me he would be back in training as normal this morning.
"He's been as good as his word on that score and that doesn't surprise me because Chris is the consummate professional.
"Clearly he will make the best decision for him and his family, because ultimately it will be the player's decision whether he stays with us or not.
"But he is a crowd favourite here and I hope that plays a part in his decision."