The Hammers are keen on the winger alongside top six rivals Southampton.
The winger only joined the Magpies from Tottenham Hotspur in the January transfer window in a move that cost them £12million.
Recent weeks have proved that deal was a wise one, as he has been the starring man in their late fight against relegation under Rafa Benitez.
Should they not manage to avoid the drop though, he has a release clause in his contract that will allow him to leave the club for £8milllion.
They have put a pacey winger among their priority signigns this summer as they look to build upon an impressive first season under Slaven Bilic.
The Hammers were interested in Townsend in the last two transfer windows but given he was at rivals Tottenham Hotspur a deal was unlikely.
His form Newcastle in recent weeks has seen them revive their interest and a move could be made if the Magpies do drop out of the Premier League.