The 24-year-old is the older brother of Celtic starlet Karamoko.
Siriki has netted five goals in 17 league games for the Posh this season, his performances attracting interest from around England and Scotland.
The Scotsman sister title ‘Peterbough Telegraph’ have been told by the club’s director of football Barry Fry that Rangers have had the player watched, while Celtic, Fulham, Newcastle United and Stoke City have all been linked with Dembele recently.
Posh expect interest to increase in January when the window opens, but the club are keen to hold on to him until the end of the season.
“Rangers have watched Siriki twice as have the Scottish national side,” said Fry. “Newcastle manager Steve Bruce watched him at Crewe when he didn’t play well.
“There will always be interest in players like Siriki, but we don’t have to sell him. We have him for another 18 months and we’d rather he stayed until the summer when we can reassess his situation.”
Dembele’s contract, it is understood, doesn’t expire until 2022.
Described as a “phenom" by the club’s owner Darragh MacAnthony, the player will be familiar to Celtic with his younger brother Karamoko on the books and having worked with Gavin Strachan, who is now part of Neil Lennon’s coaching staff.
It is not the first time Celtic and Rangers have been linked with a Peterborough United star with striker Ivan Toney talked about as a possible summer signing before he joined Brentford.