According to 90min, the Irons will follow up on their long-standing interest in the 26-year-old this summer.
With the Clarets’ Premier League status in jeopardy, the Hammers may be able to sign the player for a fee of around £15m.
Moyes needs players to occupy the central midfield role, as the Hammers have relied on Declan Rice and Tomas Soucek for the majority of this season.
With the news that the England international won’t sign a new deal and the future of the Czech Republic ace uncertain following his contract talks being put on hold, then a new midfield addition is a must.
Brownhill would make the perfect heir to the latter as they both have similar attributes, and Moyes could pull off a masterstroke by signing the “energetic” Burnley maestro, as hailed by Sky Sports pundit Lee Hendrie.
The Czech international offers more of a threat going forward, having scored five goals this season, whereas Brownhill only has two, but the Burnley midfielder has provided two more assists than the West Ham colossus.
These figures suggest that Brownhill could be the perfect replacement for Soucek if the 27-year-old were to leave the London Stadium, with his offensive and defensive abilities being very high.
The £6.3m-rated Clarets midfielder won’t come cheap, but Moyes could well have a wonderful talent on his hands if he makes the move.