Nocerino is understood to be having a medical after agreeing a loan deal and Borriello is also heading to London for talks.
Nocerino, who has 15 caps for Italy and has also played for Juventus and Palermo, has played 16 times for the Rossoneri this season but the 28-year-old may be surplus to the requirements of new coach Clarence Seedorf.
Roma remain reluctant to see Borriello, 31, leave on a permanent basis but could sanction a loan switch for the forward who needs regular games to force his way into the Italy squad for the World Cup in Brazil.
Genoa were also reported to be interested in the striker, who has started just six times for the Giallorossi so far this season.
Hammers manager Sam Allardyce is desperate to bolster his squad after a recent run of poor form which has seen them slip out of the FA and League Cups and into the third relegation spot in the Premier League.