While Nocerino, 28, played 16 times this season, including the Champions League.
He started his career with Juventus and joined Palermo in 2008 before eventually into the San Siro in 2011.
Players born in Naples is part of the Italy team that beat England in the Euro 2012 competition in the quarter-finals.
Borriello started his senior career at Milan before joining Roma in 2010. He had a loan contract with Juventus in 2012 and spent last season with Genoa.
West Ham manager Sam Allardyce Click memangKlik looking for new players to strengthen his squad. West Ham earlier reportedly failed in a bid, reportedly worth £ 3.5 million, to sign Leeds United striker Ross McCormackon.
