The Reds’ star midfielder has a year left on his current deal and negotiations over an extension are ongoing.
Head coach Struber said: “We are always in a good exchange with Alex and I think we will find a good solution in the next time.
“It is clear Alex will stay here in Barnsley for longer.”
Callum Styles, 20, played alongside Mowatt in central midfield on Saturday in the 2-1 friendly loss at Newcastle United.
Styles said: “He is an inspiration and a really good player with massive experience. He helps me in games and he is good to play alongside. Hopefully we can play together this season.”