Werder hoping Di Santo will stay
The Argentine striker is one of four players to have scored six goals in the Bundesliga this season, more than he has achieved in each of the past two league campaigns.
Di Santo's form for Werder has sparked speculation regarding his future, despite insisting himself that he is happy and enjoying life in Bremen.
"It's great that we have a player who is sought after," Schroder said. "Everyone watches the games on TV.
"He's a complete player.
"For us it is certain, he will always play, meanwhile with other top clubs he could not, and quickly became the number 15 or 16 or not in the squad."
Di Santo, who joined on a free transfer from Chelsea in 2013, has a contract until 2016 with Werder and head coach Viktor Skripnik hopes he sees out that deal.
"I am convinced that many want him in the Bundesliga," he said.
"I would be happy if Franco would stay with us for a long time.
"But I'm careful. South Americans always want to play at the top clubs."