The Hammers have been chasing the former England Under-21 international as they desperately search for a frontline forward to replace the injured Andy Carroll.
But manager Gus Poyet insists Wickham, who scored five vital goals in Sunderland’s last six matches to keep them up last season, is not for sale.
“There has been an offer for Connor but he is a player we want to keep,” Poyet told Sky Sports.
“He was a massive part of our miracle last year. He showed he is ready to play in the Premier League and I am looking forward to playing him this season.
“He’s had a great pre-season and if we started the season now he’d be in the starting line-up. I will try my best to keep him. He’s a very important part of our plans.”
Wickham, 21, signed for the North-East club for over £8million in 2011 but fell out of favour with previous managers Martin O’Neill and Paolo Di Canio.
But he enjoyed resurgence under Poyet last season, scoring 15 goals with striker partner Fabio Borini.
Borini returned to Liverpool after his loan deal expired at the end of last term but Poyet remains confident of signing him on a permanent basis after a fee was agreed for his transfer earlier this summer.
He said: “He’s a player we know very well and is important to the fans and to us both on and off the pitch. We are still confident in the next few days we can do something with him.”