The Rovers striker is chomping at the bit to get his first start for the club after coming off the bench against Bolton Wanderers in midweek.
Best reports no reaction to his ten minutes at the Reebok and has been fine in training since then which gives the manger some much-needed options up front as Colin Kazim-Ricahrds is injured and fellow striker DJ Campbell is cup-tied.
"I think the most pleasing thing is Leon," said Appleton on Friday afternoon. "He got his ten or so minutes on Tuesday and has come out of it unscathed and no reaction so that was positive.
"He has trained well since so again, with no reaction, so he certainly comes into contention.
"Whether he starts the game or comes off the bench remains to be seen. We'll monitor that over the next 24 hours."
This Sunday's game comes a little too soon for two other players who resumed training today - Josh King and David Dunn, whilst Martin Olsson is hoping to receive the green light to start training again next week.
"Josh King has trained for the first time today but we are talking about a player who had six weeks out with a hamstring and then another six weeks with the same injury," added Appleton.
"So that one is a little bit more delicate, we have to be very careful with that one. Ultimately it will come down to the player on the day.
"So maybe that one is a little bit too soon, we'll have to wait and see.
"With Dunny, again he had his first training session this morning so that is pleasing as we've not seen much of him aside from a little spell in a previous round against Derby County.
"With Martin Olsson, he sees a specialist on Tuesday which may give him the okay to join in training again. The outcome of that will hopefully be a positive one.
"So players are starting to filter back in. For the majority of them this weekend seems a little too close.
"But with ten games to go I'd like to think over the remaining ten games of the season in the league we might start seeing a little bit of a resemblance of what Blackburn could do either do between now and the end of the season or if not then certainly next season."
David Jones, Cameron Stewart and Josh Morris join Campbell in being cup-tied whilst Lee Williamson and Dickson Etuhu remain absent through injury.
The manager is expected to select from: Kean, Orr, Givet, Lowe, Best, Rhodes, Pedersen, Murphy, Markus Olsson, King, Dann, Nuno Gomes, Rekik, Goodwillie, Henley, Sandomierski, Hanley, Bentley.
Tickets for Sunday's cup tie will be on sale at The Den from the North Stand ticket office from 12 noon.
Prices are £20 for Adults, £11 Seniors aged 60 and over, £10 for Juniors under 16.