McSheffrey has been in caretaker charge since the dismissal of Richie Wellens earlier this month and was one of two candidates who were interviewed as part of a second stage of discussions.
“We’ll discuss things tomorrow with the board,” he said following the 3-0 defeat to Sunderland.
“I’ve got a meeting tomorrow and we’ll find out their decision.”
When asked if he expects to be handed the reins permanently, he said: “I don’t fully expect it.
“It’s their decision and there were a lot of candidates with a lot of quality managers who put their names in the hat.
“And we’ll see what the board’s decision is tomorrow.”
Despite Rovers’ current plight, sitting second bottom of League One and six points from safety, McSheffrey believes the job has been highly sought after.
“It’s a good opportunity for whoever,” he said.
“There are only a certain amount of pro clubs in the country that you can manage.
“A lot of managers are out of work at the moment and they want a job.
“It’s an opportunity and a challenge that a lot would want and a lot would cherish.
On the challenge of keeping Rovers in League One, McSheffrey says the next two fixtures against fellow strugglers Morecambe and Fleetwood Town are vital for giving them a platform for survival.
“We need to win games,” he said.
“We go to Morecambe and Fleetwood come here and they’re the key fixtures we need to start winning and build momentum.
“It’s not going to get easier as the months go by. There’s some big teams to come here and it’s a busy February, playing quality teams.
“A couple of wins back to back would be nice. But we take it one game at a time and we focus on Morecambe and how we prep to go and beat them.”
Rovers were comfortably beaten by the Black Cats at the Eco-Power Stadium with Ross Stewart scoring from the spot after Branden Horton brought down Leon Dajaku, while Elliot Embleton netted before the break and Ben Blythe turned into his own goal early in the second half.