The 23-year-old, who netted against the Reds three times in League One while with Scunthorpe United, is on loan at the Keepmoat Stadium from Sheffield United, where he has struggled to hold down a first-team place since a £2m return to his first club.
A move across South Yorkshire has worked wonders however and Sharp has netted five goals in eleven league appearances to date this season, sparking interest in his services with the January window approaching.
"We'd love to keep him for the season but if that's not the case then at least his loan period has helped everyone concerned," Rovers boss Sean O'Driscoll told the Yorkshire Post.
"It will have helped Billy get his career back on track, it will have helped Sheffield United, and he's helped us, so we can't complain."