Burke made the temporary switch to Celtic in January and is due to return to his parent club West Brom at the end of the season.
The 21-year-old made only three Championship appearances before travelling to Scotland, where he has settled into life perfectly at Parkhead.
Four goals and one assist in nine league appearances reflect a good start in Glasgow, where Burke has a terrific chance of winning the league and Scottish Cup.
He remains Scotland’s most expensive player in history following his £15million move from RB Leipzig to the Baggies in 2017, but still has a lot of developing to do.
As a result, former Liverpool and Scotland midfielder Don Hutchison believes Burke should bide his time at Celtic – but because he sees the 49-time Scottish champions as a breeding ground for up-and-coming players, comments which may infuriate some Hoops fans given their success down the years.
“There’s no need for Ollie Burke to move away from Celtic,” Hutchison told Radio 5 live.
“At the present time, the form he has been in [is] not amazing form but better form from where he was a year ago.
“He probably wouldn’t get in most Premier League sides at the moment, not starting anyway.
“So this is no disrespect to Celtic but it’s a great place for Ollie Burke to try and improve, play well, have an atmosphere and a crowd that are going to drive him on.
“In Neil Lennon, or whoever it may be in the summer, [he has a coach] that will drive him on to the next level.
“If I was giving Ollie Burke advice, I’d say stay at Celtic as long as you can.
“That is the place for you to learn your trade and get yourself to a high level.”