The England international, who had a spell out on loan at Sheffield Wednesday last season, has been linked with a return to Hillsborough, while Bolton are also thought to be chasing the former Ipswich man.
However, Wickham insists he has not plans to leave Sunderland and is determined to fight for his place at the Stadium of Light.
"I don't have any plans to move away," Wickham told The Journal. "I want to break into this team, into a Premier League side. That's my aim for this season.
"It's just down to myself to get into the team, no one else can do it but me.
"So my aim is to stay here and work hard, and get into this manager's team. I hope he wants to get the best out of me. He wants to help me every day, he tells me where I can improve.
"It's when a manager stops trying to help you that you need to worry. For me, the manager's doing all he can, he's given me a fair crack on the training pitch.
"He's always watching, and trying to help the strikers especially. So it's a good chance for me to show him that I'm capable of doing the things he needs."