Armstrong has sparked off a furious race for his signature this summer after another impressive last season in the Championship.
Blackburn finished in the bottom half of the league table, but Armstrong scored 28 goals in the Championship, taking his tally to 46 strikes in the English second tier over the last two campaigns.
Everton and West Ham have been credited with an interest in Armstrong, while Norwich have now joined the chase for the 24-year-old.
But it has been claimed that Southampton have the edge in the race to sign the forward this summer.
The Saints are in the market for a striker amid uncertainty over Danny Ings’ future on the south coast.
Armstrong has emerged as one of their top targets and Southampton are pushing to take him to St. Mary’s this summer.
Blackburn are prepared to cash in on Armstrong, but only for the right price.