West Ham will reportedly listen to offers for Michail Antonio and Cheikh Kouyate but have rejected bids from Fiorentina and Atalanta for midfielder Pedro Obiang.
Sky say the Hammers are looking for more than £15m for Antonio (pictured) and around £10m for Kouyate, who featured for Senegal at the World Cup.
But the club have snubbed bids for Obiang.
Recently-appointed boss Manuel Pellegrini is keen to revamp the squad and wants Sporting Lisbon’s Bruno Fernandes and Lazio’s Felipe Anderson to join Jack Wilshere at the London Stadium.
West Ham have confirmed the signing of Wilshere on Monday.
The 26-year-old midfielder – a West Ham fan as a boy – has moved on a free transfer after recently leaving Arsenal at the end of his contract. Wilshere has signed a three-year deal.
“It feels good, it feels special,” Wilshere told West Ham’s website. “Many people know that I’ve had a special bond with this Club growing up.
“People will have seen the picture of me in a West Ham shirt and I’ve got good memories of my childhood supporting West Ham, watching them at Upton Park.
“It feels good and of course my family and a few of my friends are West Ham fans so everyone’s buzzing.”
The England international, who has played 34 times for his country, will fly out to Switzerland to link up with the West Ham squad at their pre-season training camp in Bad Ragaz.
Hammers director of football Mario Husillos said: “Jack is a player with vast experience and quality at the highest level, having played all of his career in the Premier League.
“He is a passionate man and has shown winning characteristics throughout his career.
“Jack will be a great addition and we look forward to seeing his undoubted quality in a West Ham United shirt over the coming years.”