The 24-year-old is a product of the Old Trafford academy system but was deemed surplus to requirements after just five senior appearances for the Red Devils.
He was allowed to make a loan deal at Turf Moor permanent in January 2015, having previously taken in spells at Leicester, Derby and Blackburn.
Keane has gone on to become an England international and a proven Premier League performer, with Pallister talking up his credentials amid talk of a possible big-money bid from United.
“It’s easy to say is it an expensive mistake to have let them go,” the ex-United defender said in the Daily Mirror.
“When you’re told you are going to leave United it can be hard to bounce back.
“But he’s gone away and improved himself, becoming an England international.
“If the next step is to come back, he already knows the place and will return a better player.”
United brought one familiar face back to the club last summer in Paul Pogba, with the world transfer record broken to re-sign him from Juventus.
Keane is now among those reported to be on Mourinho’s summer wish list, although fellow centre-halves such as Marquinhos of Paris Saint-Germain and Real Madrid’s Raphael Varane have also been mooted as possible targets.