Robson is a free agent after cutting short his stay in Major League Soccer with Vancouver Whitecaps.
The 34-year-old, who left the Riverside to join Vancouver in June last year, is back training with the Championship side, but Mowbray has rejected suggestions that could lead to the offer of a contract.
Mowbray said: "First and foremost it's not something that's on my mind, it's not something I've even thought about. He made the decision to take his career somewhere else."
"Barry's been away for six months and he just rang me to ask if he could come to the training ground to keep fit."
"I don't know what his long-term plans are, I don't know what his expectations are, I don't know anything about his current situation."
"People don't understand the balance of a squad. I'm not in the business of adding players just for the sake of it."
"We've moved on since Barry left, we've brought new players in and my consideration is managing them."
"We're just helping Barry out. He contacted me and asked if he could train with us to keep fit. It's a reciprocal thing. He was a good professional when he was here, he trained hard and gave his all in games, so we are happy to help."