Sean Dyche would not be interested in becoming Rangers head coach at this time, Sky Sports News understands.
The 54-year-old is currently without a job and worked with Ibrox sporting director Kevin Thelwell in his last role at Everton.
Rangers are still in the process of drawing up a list of potential successors to Russell Martin, with no clear outstanding candidate so far.
Please use Chrome browser for a more accessible video player
Highlights of the Scottish Premiership match between Falkirk and Rangers
Martin was sacked on Sunday after having to be escorted out of Falkirk’s ground by police to protect him from a group of Rangers supporters following a 1-1 draw.
He led the team to just one win in their first seven league games, matching the club’s worst-ever start at this stage of a season.
It is thought several members of the Rangers board had been ready to sack Martin earlier in the campaign but others had wanted to see if he could turn things around.
Please use Chrome browser for a more accessible video player
Sky Sports’ Kris Boyd reacts to Russell Martin’s sacking after 123 days, and who should be next to take charge at Rangers
The preferred choice among many supporters appears to be a return for Steven Gerrard but it is not clear how feasible that is at this stage.
Hearts’ Derek McInnes is believed to have admirers at Ibrox but his side are currently top of the league after an unbeaten start.
Under Martin, Rangers also dropped out of the Champions League after their joint-worst European loss as they were thrashed 6-0 away to Club Brugge in the play-off, losing the tie 9-1 on aggregate.
The Ibrox side found themselves in the Europa League, which also started with two defeats against Genk and Sturm Graz.
Please use Chrome browser for a more accessible video player
Former Rangers assistant manager Gary McAllister refused to rule out a return to his former club
Despite League Cup progress, where an Old Firm semi-final awaits, Martin won just five of his 17 matches, meaning he departs as the worst-ranked permanent Rangers boss.
Martin is also the shortest-serving manager in Rangers’ history and the fourth to be sacked within the last three years.
Next up, Rangers are at home to Dundee United after the international break on October 18.
Rangers’ upcoming fixtures
- Dundee United (H) – Scottish Premiership – October 18
- Brann (A) – Europa League – October 23
- Kilmarnock (H) – Scottish Premiership – October 26
- Hibernian (A) – Scottish Premiership – October 29 – live on Sky Sports
- Celtic (N) – League Cup semi-final – November 2