After joining the club on loan in January, Jones played in 15 games and as a result has established himself in the squad.
As well as the player wanting a return, Steve Kean, the club's manager, does not want to lose him.
Jones expressed his intention to return by telling The Sun: "It was a good time for me at Blackburn. Now I need to look at what happens.
"My team in Germany have told me to come back but my agent knows what I want.
"I've been talking with Steve Kean and he needs to talk to the owner."
Schalke may be looking to keep the player as they need to build their squad. Although the team reached the semi-finals of the Champions League, they finished a poor 14th in this season’s Bundesliga.
With funds coming in from the sale of star goalkeeper Manuel Neuer, it is unlikely the club will be desperate for the money coming from Blackburn.