Nocerino, 28, who has 15 caps for Italy and featured at Euro 2012, began his career at Juventus and also played more than 100 league games for Palermo.
He joined Milan in 2011 and scored 11 goals in his first season but has only made 11 appearances in Serie A this term.
Borriello, 31, has been capped seven times and has scored nearly 100 goals after spending a decade in Serie A at a number of clubs including Milan and Juventus.
After spending last season on loan at Genoa he returned to Roma this term, netting once in 11 appearances.
The pair could make their debuts for third from bottom West Ham at third-placed Chelsea in the Premier League on Wednesday.
(Reporting by Martyn Herman and Josh Reich, editing by Tony Jimenez)
