Armstrong spent the second half of last season on loan to Blackburn, for whom he scored nine goals in 21 games en route to promotion from League One.
And the newspaper reports Rovers have agreed to pay an initial £1.75 million for the Newcastle striker, with another £1.25 million due if performance-related clauses are triggered.
Armstrong is said to have had interest from a host of Championship clubs, but looks set to reunite with Tony Mowbray for a third time, after the Blackburn boss worked with him at Coventry City.
The 21-year-old's anticipated exit follows Newcastle's £9.5 million capture of the former Mainz striker Yoshinori Muto ion Thursday.
Academy product Armstrong made 21 appearances in Newcastle colours, but failed to score for his boyhood club.
Is Armstrong a good addition for Blackburn?