Whitehead is available on a free transfer after seeing out his contract at Stoke earlier this summer.
A number of Championship clubs are thought to have expressed an interest in the 31-year-old, with the player now weighing up his options.
Mowbray has held talks with former Sunderland captain Whitehead and hopes he can persuade him to move to The Riverside.
"I feel he could help solidify us out of possession," Mowbray told the Evening Gazette.
"Can we do it? I think the boy has got options but he's somebody we've talked to and we'll see what develops over the next few weeks."