The 24-year-old scored a hat-trick in the final game of the season as Rovers won 5-2 against Birmingham City on Saturday.
His goals on the day took his overall tally up to 29 goals in all competitions, in a season that started with plenty of promise for Blackburn, but ended up tailing off over the course of the campaign, leading to them finishing in 15th.
Whilst speaking on BBC Radio Lancashire after the game, Blackburn manager Tony Mowbray admitted that the club would be open to selling Armstrong in the coming transfer window.
"For Adam's sake let's hope the phone rings and someone offers us a ridiculous amount of money," he said.
"We shake him by the hand and we say 'go and bang in loads of goals in the Premier League.'"
Armstrong has been one of the best players in the whole Championship this season, ending the season with a remarkable record of nine goals and two assists in his last six games of the season, leading to him finishing just three goals away from Ivan Toney, who won the top scorer award for the season.
West Ham are in need of a striker to challenge Michail Antonio, especially with the prospect of European football next season, and Armstrong's experience in English football could be a prized asset for the Irons.
Newcastle are keen on signing a striker to partner last summer's signing Callum Wilson, whose goals have been crucial to helping them potentially avoid relegation this season.
Whilst playing regularly for Newcastle might seem as the more reasonable option, being his hometown club and the team that he joined Blackburn from in 2018 for €1.9 million, the prospect of playing in Europe could be too good of an opportunity to turn down for the 24-year-old.
According to transfermarkt.com, Armstrong's current market value is at €16 million, and given his excellent finish to the season, his value might increase over the coming weeks.