The Dutchman has been brought in to replace sacked Luiz Felipe Scolari until the end of the season.
But Ballack wants him to remain at the club beyond the end of this season.
The German international told reporters: “It’s always good for a team if you have consistency. At the moment, the situation is clear – the coach has a contract with Russia and everyone respects this.
“But in football a lot of things are possible. If we have success with him, maybe he’ll want to stay.
“We are happy with him. We hope he can stay longer with us but it’s his decision.”
He added: “Chelsea’s strengths were always our commitment and power but we lost it a little bit in the last few weeks.
“We never had the style of a team like Arsenal, who played more football, but we had the power and commitment. We have to try to get back to that.”