The Republic of Ireland international joined Rovers from Newcastle United last summer, but is yet to feature for the club because of a knee injury that he suffered shortly after his arrival.
He stepped up his recovery by scoring during a reserve match yesterday afternoon, but Appleton has admitted that he will not push the 26-year-old too much between now and the end of the season.
"In an ideal world I would have been thinking solely about Leon Best for next season and nothing else, but we don't live in an ideal world," the boss is quoted as saying by the Lancashire Evening Telegraph. "If you asked Leon, he is chomping at the bit and will probably expect to start on Saturday, because of the type of character he is.
"Realistically he has been out for a long, long time. He has not played that many games because he had the injury previously to his cruciate. He has not played a lot of football in the last 12 to 18 months.
"So we have to be slightly cautious with him, make sure we look after his best interests not just the football club's."
Reports have claimed that Best could be included in the Blackburn squad for Saturday's match against Peterborough United.