The 19-year-old midfielder has quickly become a fans’ favourite at the Keepmoat Stadium after arriving on loan from Anfield in the summer.
He has started 11 out of 13 League One games, helping Grant McCann’s side to fourth in the table.
But Kane – who is due to return to the side for today’s visit of Gillingham after serving a one-match suspension— is only on loan until January.
At a club where 23 players will be out of contract next summer nothing is certain, but talks between Rovers and Liverpool are ongoing with a view to extending the loan until the end of the season.
“I’d love to stay and hopefully get the team promoted,” said Kane. “I’m enjoying it. I’m playing much more than I expected to play. I’m loving it here.
“I’m enjoying every game and every game is a new and different experience.
“Hopefully I can carry on playing and we can stay near the top of the table and get promoted.”
Rovers have won six out of their last eight games, but suffered a heavy 4-0 defeat to Fleetwood Town on their last home game in League One.
Today they host a Gillingham side who have emerged winners just once since the first week of the season – although that was at leaders Portsmouth earlier this month.
“It’ll be a massive test,” said Kane. “Every game is a tough game in this league.
“Hopefully we can put on a good performance, get three points and chase down the top three. There’s a positive vibe among the group at the moment.
“It’ll be a tough game against Gillingham, but I think we’re ready for it.”
Whatever division Doncaster are playing in next season they will face some big decisions over squad make-up between now and the summer.
McCann met chairman David Blunt and chief executive Gavin Baldwin on Thursday to discuss plans for the January window, including the future of loan trio Kane, Jermaine Anderson (Peterborough United) and Mallik Wilks (Leeds United).
“We’ve had discussions with players,” said McCann. “I’ve had discussions with players who are approaching the end of their contracts.
“I’ve planted the seeds with them.”