The former Newcastle United forward, who is this season's League One top goalscorer netting 24 times, has been targeted by a number of clubs in this summer's transfer window.
Old Firm pair Celtic and Rangers have both been linked with the 24-year-old and the Birmingham Mail reports that the Baggies are to rival both Scottish clubs, with Peterborough chairman Barry Fry suggesting that potential suitors would have to pay around £15m for his services.
"I've had agents on telling me that Rangers and Celtic are very interested. But I haven't had any calls from either Rangers or Celtic, personally," the 75-year old said.
"If they have any sense, they'll pay us £15m to get him. If they haven't any sense at all, then I won't be hearing from them."
The EFL confirmed earlier this week that the 2019-20 League One campaign would be curtailed, with Peterborough missing out on a playoff position due to a points-per-game system deciding the league's outcome.
Fry admitted back in April that the Posh would find it very difficult to keep hold of Toney if they didn't win promotion. body check tags ::