The 19-year-old Germany midfielder recently penned a new five-year contract with his home-town club, yet that has not brought an end to speculation about his future.
Chelsea are among the clubs linked with a move for the youngest ever player to make 100 appearances for Schalke.
And Tonnies admits even his club's biggest asset has a price.
"Of course we want to keep hold of him, Julian is an important figure in Schalke," he told the Express newspaper.
"But if we want to be fair with him, then maybe we have got to consider letting him move abroad sooner or later.
"If somebody like Real Madrid were to enquire about him, what should I say? Don't talk to them? Get serious."