The Hammers have made three summer signings already, with Darren Randolph, Petro Obiang and Dimitri Payet all arriving so far.
New manager Slaven Bilic is now trying to make a fourth new signing, with The Sun reporting that Liverpool outcast Borini is set for a permanent move to Upton Park.
Borini, 24, has struggled to make an impact with Liverpool since arriving from Roma in 2012, scoring just three goals in 38 games in all competitions.
A ten-goal season-long loan spell with Sunderland showed what the Italian can do, and it seems that West Ham are willing to pay up to sign the former Chelsea forward permanently.
The Sun report that Borini is set to arrive in London for talks and a medical with West Ham within the next 24 hours, with a deal expected, according to the report.
Assuming that flop Mauro Zarate leaves West Ham for good this summer, Borini could actually bring something different to the West Ham front line.
With Enner Valencia providing pace, Andy Carroll providing a target man figure and Diafra Sakho providing all-round athleticism, there is room for a more technically-gifted forward.
That's what Borini can do, in that he can drop off a front man and use the ball well, or he can play as more of a poacher inside the box. Somebody needs to turn Borini's career around, and that could well be Bilic - if the Italian forward is used correctly at West Ham.