The Hammers are one of a number of clubs keen on the 24-year-old who has been sensational this season in the Championship.
However, the North East club could hold an advantage in the pursuit thanks to a clause in his contract which would see a 40% sell-on written off as part of any deal.
Newcastle are currently teetering above the Premier League relegation zone with goals hard to come by as Steve Bruce’s men fight for top-flight survival.
The Magpies are believed to be ready to push ahead with a deal for their former frontman regardless of what league they are in next season.
For £16million someone is going to land a bargain in the in-form frontman.
The Hammers have previously been almost at the front of the queue for Armstrong, but the clause in place could ultimately prove a major financial stumbling block.
There remains hope that should Newcastle be relegated, the player could want a Premier League move – something that could keep the Irons in the mix.