The 31-year-old was been released by new Potters manager Mark Hughes earlier this month and is understood to have attracted interest from several potential employers since.
Mowbray revealed the Teessiders have held talks with Whitehead and are waiting to see what develops, although the player's wage demands could prove problematic.
Mowbray told the Evening Gazette: "I feel he could help solidify us out of possession.
"Can we do it? I think the boy has got options, but he's somebody we have talked to and we will see what develops over the next few weeks."
Whitehead began his career at Oxford, but joined Sunderland for an initial £150,000 nine years ago.
He spent five seasons at the Stadium of Light, where he was named captain, before heading for the Britannia Stadium during the summer of 2009 in a £3million switch.