The midfielder Andrew Wright is likely to stay, but left-back Marcus Williams has stated his desire to leave and centre-back Andy Butler is also weighing up his options.
Wilcox is the son of former Scunthorpe player and assistant manager Russ, who followed Brian Laws to Sheffield Wednesday in 2006.
He joined the club as a youth trainee in 2005. He has yet to feature in the first-team but has impressed in the reserve side.