Rovers will start interviews for the vacant role on Monday and Tuesday, with a view to making an appointment later in the week.
The League One club have a ‘strong shortlist’ of candidates wishing to become Grant McCann’s successor, according to chief executive Gavin Baldwin.
The current frontrunner for the position is understood to be former Barnsley and Mansfield Town manager David Flitcroft, who was controversially sacked by the Stags after their penalty shoot-out elimination to Newport County in the League Two play-off semi-finals in May.
Ex-Oxford United chief Michael Appleton – who lost out to Paul Dickov when Rovers appointed a new manager in May 2013 – and Motherwell manager Stephen Robinson have also been mooted as potential candidates.
Any appointment of Moore, out of work since being harshly shown the door by West Brom on March 9 – when the Baggies were in fourth place in the Championship – is likely to prove popular with Rovers supporters.
The 45-year-old, who is understood to have applied for the position, is remembered fondly for his playing association with Rovers during a difficult era for the club in the mid-Nineties.
Moore joined the club from Torquay United in July 1995 and proved a mainstay in the club’s backline for two seasons during the ill-fated Ken Richardson era – and is widely recognised as one of the most outstanding defenders to represent the club in past quarter of a century.
Moore’s performances earned him a six-figure move to Bradford City in the summer of 1997, with the big defender helping the club to the Premier League in 1998-99.
The Birmingham-born centre-half later enjoyed a successful spell in Yorkshire at Barnsley.
Speaking earlier this week, Rovers CEO Baldwin said: “We have had strong interest and taken references across all levels. We did not choose for Grant to leave, but it’s our job to ensure we come out the process in a better position than we went into it and we are extremely optimistic.
“We have worked hard to talk to people across football at all levels about possible candidates to give ourselves the best chance of the best possible manager.”