Rangers aim to appoint a manager in the coming week, director Paul Murray has told BBC Scotland.
Stuart McCall replaced Kenny McDowall in March, on a deal until the until the end of the season, which ended in play-off final disappointment.
McCall has made it clear he wants to stay on as Rangers prepare for a second campaign in the Championship.
Former Brentford boss Mark Warburton has had talks with the Ibrox club and is interested in taking the role.
"Our plan is to make an appointment next week," said Murray, who returned to the club's board in March.
It is likely Warburton, 52, would take his Bees assistant and former Rangers captain David Weir with him should he get the job.
Confirming he had held talks with the Glasgow club, he told BBC Scotland last week: "Any job that myself and Davie Weir would look at would be about going in, having a project and being able to add value.
"But I'm sure a club like Rangers has got a big search process under way.
"I'd like to think we have shown the attributes required to do a good job at a football club."
McCall, who is currently working with the Scotland squad ahead of next weekend's Euro 2016 qualifier with the Republic of Ireland, won six titles as a player at Ibrox in the 1990s.
"I would say my strengths as a manager are recruiting, improving people and getting the best out of them," said McCall, immediately after the 6-1 aggregate defeat to his former club Motherwell.
"That's what Rangers will need next season, whoever the manager is."
The 50-year-old won seven and drew six of his 17 games in charge.