The Italy internationals are expected to travel to London for talks and medicals over the weekend as Hammers boss Sam Allardyce finally closes in on signing some experienced players in the transfer window.
Roma striker Borriello, 31, has struggled for regular games in Italy this season and wants to go out on loan to get some action, while midfielder Nocerino has often been overlooked at the San Siro in Serie A and has usually had to settle for a place on the bench.
Widespread reports, in both England and Italy, suggest the deals are close to being agreed, and the pair are expected to be confirmed by the Hammers early next week or even over the weekend.
Borriello, who has seven caps for Italy, has managed just one goal for Roma this season but has not been first choice in the capital and would improve Allardyce's attacking options considerably in the second half of the season.
Nocerino would also be viewed as a good addition as the former Juventus and Palermo man has been a regular in the Italy squad in recent years, playing a key role in the engine room as the Azzurri made it through to the final of Euro 2012.