Jones joined Blackburn on loan until the end of the season from Schalke during the January transfer window.
“I think Jermaine’s been in this form for a number of weeks,” Kean said.
“At times it looked as though there were two of him in there. He was getting back, he was screening Kevin Davies, he was pushing up into midfield.
“Then he was driving on, that’s the type of energy he’s got. I thought he was absolute quality.
“We’re desperate to keep Jermaine and he wants to stay. We tried to fix a price with Schalke, but we couldn’t so we’ve just got an agreement with Schalke until the end of the season.
“And if we can do some good business then hopefully he’s going to be a Blackburn Rovers player for pre-season.”