The midfielder has impressed in both cup outings against Millwall and Appleton is hoping Dunn maintains that level for the remaining ten league games of the season.
"I think he has shown enough in the last game and a half to know that he has got enough ability to make sure he stays in the side," said Appleton.
"We just need to keep him fit, that is the biggest thing because he could be very influential for us over the remaining ten games.
"From his point of view he's got ten games to prove that he deserves the opportunity to get a new contract.
"I think if he performs the way he has done in the last one and a half games then he'll certainly be in with a very good shout."
See Dunn in action against local rivals Burnley this Sunday. Tickets for the 12.30pm match are currently on sale to Rovers supporters with a database history of purchasing tickets.
Prices are from £25 Adults, £17 Seniors and £12 Juniors.
Supporters are reminded that this is an all ticket match, there will be no sales on the day of the game.