Keller replaced Huub Stevens last December on a contract until the end of the season and, after some initial difficulties, has taken them to fourth in the table.
With Armin Veh ruling himself out of the running by signing a new deal at Eintracht Frankfurt last week, the list of candidates to be Schalke coach next season is diminishing.
However, Tonnies says Keller's name is still on that list.
"If we are successful, then this is the most important indication our coach is doing a good job," he said.
"Jens Keller has a good chance of remaining coach here beyond the summer."
With seven games of the season to go, Schalke are on course for Champions League qualification and this remains the club's objective.
And Tonnies paid tribute to Keller's work after his side's 3-0 win over Hoffenheim at the weekend.
"We believe in Jens Keller," he told Sport Bild magazine. "It's a shame he was not given a chance when he took over, but I am sure he will prove himself to everybody.
"Our aim is the Champions League and we're all working towards that."