On Thursday evening, the German had told the club he no longer wished to be considered for the position.
But the dramatic collapse of Kevin Muscat’s return to Glasgow on Sunday night has changed the picture.
The Rangers Review says that talks are now set to finalise his move to Ibrox on the eve of the Europa League fixture with Brann on Thursday evening.
Rohl was interviewed for the post earlier this month and impressed the Rangers delegation.
The former Sheffield Wednesday manager was in the running before Martin’s appointment in the summer.
Rohl was eager to get down to business last week ahead of the return to Premiership action against Dundee United.
A lengthy recruitment drive saw the board turn their attentions to Muscat and a deal was all-but done before a late change of heart left supporters stunned.
Ibrox sources have indicated that the discussions reached an advanced stage.
But it has been suggested that the practicalities of the move have made it unworkable to all parties while Muscat looks to lead Shanghai Port to the Chinese Super League title in the coming weeks.
Muscat was part of Alex McLeish’s squad that won the treble in 2003 and was poised to return to Ibrox after forging a name for himself as a manager.
The Australian is seeking to lead Port to the Chinese Super League title this term and add to the medals he collected with Melbourne Victory and Yokohama F. Marinos.
It’s understood chairman Andrew Cavenagh is keen to sign off on an appointment in the coming days.
And that could lead to Rohl being given the chance to salvage a season that is threatening to spiral out of control.
Steven Smith oversaw the draw with United at the weekend as Rangers fell further adrift in the title race.
James Tavernier rescued a point at Ibrox after United came from behind to lead following Thelo Aasgaard’s opener.
Patrick Stewart, the chief executive officer, and sporting director Kevin Thelwell came in for more criticism from supporters during the fixture.
A message reading “Stewart, Thelwell pack your bags and go before we pack them for you” was displayed at half-time in the Sandy Jardine Stand.
The players were also in the sights of the Union Bears, who displayed a banner stating “No more buses to hide on. No more managers to hide behind. Face your failures like men,” in the first half.