Inter Milan midfielder Joao Mario is expected to make a decision on West Ham's offer early next week.
Inter Milan will assess their options before taking a call Wolverhampton Wanderers linked Andrea Pinamonti's future at the San Siro.
West Ham and Everton wing target Nicolas Gaitan has also been offered to Serie A giants Inter Milan.
Inter Milan are unlikely to make a move to sign West Ham wing target Andre Schurrle this month in a boost to the Hammers' signing hopes.
Serie A giants Juventus, Inter Milan and Roma have been keeping tabs on Manchester United midfielder Marouane Fellaini.
Liverpool and AC Milan linked Barcelona midfielder Rafinha has been offered to Inter Milan.
Chievo have joined the race for Wolverhampton Wanderers target Andrea Pinamonti, who currently plays for Inter Milan.
Inter Milan have entered the growing list of suitors for Manchester United and Liverpool midfield target Leon Goretzka.