Along with fellow mackem Graham Kavanagh, also this week linked with a Carrow Road switch, Connolly was Sunderland boss Roy Keane's first signing, the pair arriving from Wigan before the end of the summer transfer window in 2006.
Connoly netted 13 times last term as the Wearsiders ascended to the top flight, but has failed to hold down a first team place at the Stadium of Light since the arrival of Kenwyne Jones and Michael Chopra.
Leicester are also said to be interested in Connolly and Kavanagh.