The 40-year-old former England international has taken charge of the No.6 role during Albion’s recent resurgence.
But he is putting in the hours with Baleba around the training ground.
Milner recently said he would love to play ten games alongside the young Cameroon international as part of his development.
Instead, it has tended to be one or the other on the pitch at any one time.
Asked whether Milner is having a big influence on Baleba, head coach Fabian Hurzeler said: “Yes, definitely, and I think being together with James Milner for 12, 13, 14 hours is always an education, especially for the young players because they see what it needs to train on the highest level, see what it needs to prepare on the highest level.
“It’s not only on the pitch regarding communications, it’s also beside the pitch regarding behaviour, and it’s definitely a thing where all the young players benefit from.”
Baleba travelled but was not in the matchday squad as Albion won 1-0 at Sunderland.
He was said to have a minor issue and is likely to be pushing for a place when Milner’s previous club Liverpool visit the Amex on Saturday.
In Baleba’s absence, Milner played the full 90 minutes at the Stadium of Light.