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.
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.
Hearts' Derek McInnes is believed to have admirers at Ibrox but his side are currently top of the league after an unbeaten start.
Gerrard reveals ‘unfinished business’ in his managerial career
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.
On Tuesday, Gerrard admitted he had "unfinished business" in his managerial career and would jump at the chance to return for the right opportunity.
Gerrard - who said his time at Rangers was a "perfect match" - won the title at Ibrox in May 2021 after an unbeaten league campaign, preventing Celtic from completing 10 championships in a row, but had less success at Aston Villa and then Al Ettifaq, whom he left in January after 18 months.
"There's a part of me that still feels that there's a bit of unfinished business in terms of wanting to go in and face another couple of exciting challenges," said Gerrard, a guest on the Rio Ferdinand Presents podcast.
"But I want a certain type of challenge. If in an ideal world they come available, I'll jump at them. If they don't, I won't go back in.
"I want to be at a team that's going to compete to win because I think that suits me better.
"I know where I'm strong and I know there's areas where I need good support and I need special skill sets to make me better and stronger in terms of my staff and my group.
"I felt like I had that to a tee at Rangers. I had it to a tee. A lot of coach changes at Aston Villa and over in Saudi, I don't think helped me from a personal point of view."
Since leaving Al Ettifaq Gerrard said he had had "five or six interesting phone calls" but the timing had not been right.
Recently becoming a grandfather for the first time and not having his preferred backroom team available to him were two of the reasons he gave.
"I think certain jobs and certain clubs would suit my style and the way I like to go about it," he added.
"But I've also got time now where I'm not in a rush, where I know the right people that are out there to make me a stronger and a better coach. They're the people I need to find.
"Because if I get the right match with them people around me, I know and I've proved I can be successful as a manager and that's what I'm working on in the background now."
- 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
