Armstrong scored 28 goals in the Champions League last season for a Blackburn side that finished 15th in the league table.
His goalscoring exploits with Blackburn have led to several Premier League clubs taking a keen interest in the 24-year-old hitman.
West Ham and Fulham are reportedly frontrunners in the race to sign Armstrong and he has also been linked with a move to Everton, Brighton and Norwich City.
Southampton also hold an interest in the forward but it has been claimed that they are unlikely to sign him.
Blackburn are aware of the interest Armstong has been attracting and want a fee of £25m before they are prepared to agree to sell him.
The asking price is turning out to be prohibitive for several clubs and Southampton have been ruled out of the race.
The Saints are unlikely to want to spend a club-record fee to sign Armstrong in the ongoing transfer window.
Norwich are also one of the clubs who are expected to bow out of the race if Blackburn stick to their demands, something which means less competition for West Ham and Everton in the chase for the hitman if they choose to bid.