Armstrong has been a revelation in a deeper central midfield position under Brendan Rodgers, netting eight goals this season and becoming a regular starter in recent months.
The 24-year-old has 18 months left on his Parkhead contract and assistant manager Chris Davies is optimistic that deal will be extended soon.
“That’s something that would be really positive for the club,” Davies said. “Stu has done fantastically well over the last few months. He has really really developed in the way we would like.
“We were obviously aware of him when we came in and spoke about him and have been really impressed with his development and personality.
“The manager has made it clear to the player that he values him and how well he has done and the player is enjoying it, and everybody is happy, so that’s all positive on that front.”
Former Celtic midfielder Petrov has been very impressed with the former Dundee United player this season and feels he could command the same type of fee being talked about for Celtic forward Moussa Dembele.
“You can hardly find a more dynamic midfielder who starts deep and scores goals and create chances,” Petrov said. “Stuart has definitely matured a lot.
“When he came he was trying to do everything, he was trying to do a lot of stuff that wasn’t his game. But now you can see he learns, he moves the ball quicker, he times his runs, he starts scoring goals, and if he keeps on the same way, they will have a very good midfielder that can be another £20-plus million player if he develops the way he has been developing so far.
“He has shown he can be something special. As long as he keeps developing and working hard and stays away from injuries, he can become a very good midfielder for big clubs.
“He has shown he is a midfielder who scores, creates, is dynamic, makes a difference in the team.”
:: Stiliyan Petrov was speaking at a William Hill media event. William Hill is the proud sponsor of the Scottish Cup.