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."
Mowbray also confirmed his interest in Hungarian Jozsef Varga and former Burton Albion star Jacques Maghoma - both Sky Sports exclusives.
On Varga he said: "He's one that we've had conversations about."
And on former Spurs trainee Maghoma: "I'll talk to the boy next week. I think he's got the potential to be a decent player."
Meanwhile, Mowbray also revealed that former Chelsea fitness director Bryan English had joined the club.
"I felt we probably cut too far in certain areas regarding fitness, regarding sports science, regarding medical," Mowbray said.
"So Bryan is coming in as a consultant to help in that department.
"He's a guy who worked with Jose Mourinho at Chelsea, he's got huge experience and has worked at the very top end of English football.
"He's coming in to oversee pre-season. We talked long and hard at the end of the season about the fall off in the second half of the season.
"Bryan's going to come in and help us and see if we need to do anything different. Hopefully the expertise and knowledge he brings will help maintain the good standards we set at the start of the last two seasons."