Gillingham boss Evans was backed in to the even money favourite on Sunday to replace Grant McCann as Rovers boss following his departure to Hull City.
But such a fluctuation in the betting market has not come as a result of talks between the two parties.
Former Rotherham United boss Evans has yet to take charge of a game for Gillingham having only been appointed manager in mid-May.
Rovers have laid out their plans to stick to the same recruitment framework that saw the hirings of McCann and his predecessor Darren Ferguson, with a deadline for applications set for 5pm on Friday.
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Though keen to maintain the in-depth vetting of potential candidates, it is understood they will break from the framework and hold talks with stand-out individuals who have shown an interest in the job.
Rovers received dozens of expressions of interest even before McCann's departure was officially confirmed on Friday with chief executive Gavin Baldwin lauding the 'high calibre' of names submitting applications over the first day of the search.
One man who appears not set to submit an application is former Rovers midfielder Richie Wellens, who is the current manager of Swindon Town.
Wellens has ruled himself out of the job at this point in time, saying he owes loyalty to Swindon chairman Lee Power and the club's supporters.