The 24-year-old has been in fine form for Rovers this season, bagging 22 goals in 40 appearances during the current campaign.
He has just over a year left on his current contract, and Rovers manager Tony Mowbray hinted earlier this month that he could be sold this summer.
Mowbray has now confirmed that the club could be forced into selling their top assets to fund incoming transfers this summer.
With playmaker Bradley Dack currently on the sidelines, Mowbray’s only other hope of raising sizeable funds is by selling Armstrong.
In an interview with Lancashire Telegraph, Mowbray outlined his plans for the upcoming transfer window.
“We will have to see what the budget is like, what the salary level of the group is and see how much we’ve got to spend,” he said.
“Then we’ll have to see whether we’re going to sign free transfers, loans, or if you’ll have to sell a player to buy players.
“That’s what the summer time normally is – how are you going to improve your team for the next year?”
Armstrong has been one of the standout performers for Rovers during what has been an underwhelming campaign for the club.
Owners Venky’s previously slapped a £25 million price tag on his head, but that figure is probably over the top given Armstrong’s contract status.
West Ham have repeatedly been linked with Armstrong, while Newcastle have also been credited with an interest.
With Everton also in the running, Rovers will be eager to spark a bidding war for Armstrong’s services.
On that basis, the interested clubs would be well advised to secure a deal as early as possible.