Negotiations, which did not begin until late on Monday, between the Black Cats and the Wigan manager are almost complete and it is only a matter of time before Bruce is installed at the Stadium of Light.
"I know Steve is desperate to prove himself at the highest level. The Sunderland job could be just the vehicle to help him achieve what he wants," said Pallister.
"Anyone who has played at the highest level and been as successful as Steve is bound to be ambitious," he added.
Pallister, who played alongside Bruce in the centre of United's defence from the late 1980s to mid-1990s, knows enough about his former team-mate to be convinced he will do well back in his native north east.
He admits Sunderland, who should have plenty to spend over the summer after American businessman Ellis Short assumed full control of the club last week, is a different prospect for Bruce after years of working with tight budgets.
But he said Bruce was ready to take the step up and turn the Black Cats into a top-10 side - which Short said was his first target after taking over.
"He has a good reputation as a manager, he works hard, but wherever he has managed he has had to operate on limited funds," Pallister told the Manchester Evening News.
"Sunderland can provide a fair-sized war chest, they have a great fan base and a progressive owner and chairman (Niall Quinn).
"Steve has had his ups and downs in management at Crystal Palace and Birmingham but he just wants to manage at the highest level and challenge the best."