Milan midfielder Antonio Nocerino, 28, has already agreed a loan deal, according to reports in Italy, and a similar move for Roma striker Marco Borriello is also believed to be nearing completion.
Nocerino is expected in London on Friday for a medical and Borriello could also make the trip to complete his temporary move to England.
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 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 are also interested in the player and could yet move to keep him in Serie A after he started just six times for the Romans 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.
Haha! Borriello is rubbish (think Andy Carroll without a hammer of a left foot!). Roma have been trying to get rid of him on a permanent basis for years due to his high wages, but the best they've been able to do is loan him out as much as they can.- mikemanaman