The 21-year-old had a superb end to last season, scoring five goals in nine games for the Black Cats to help the club avoid relegation from the Premier League.
This came after the striker had spent a successful loan spell in the Championship with Sheffield Wednesday, where he scored eight goals in 11 games, and then a less impressive temporary stint at Leeds, during which he failed to score in five appearances.
West Ham are in need of a target man following the ankle injury to Andy Carroll, who is expected to be out until at least December.
The size of the Hammers’ bid for Wickham is, as yet, unknown.
Wickham began his career with Ipswich and joined Sunderland for £8m in June 2011.