David Healy, a former team-mate of Steven Davis with both Rangers and Northern Ireland, has said the former midfielder would be "an asset" if he were to become part of the backroom staff at the Scottish Premiership giants.
Davis has been linked with a coaching role at Rangers should Steven Gerrard return for a second spell as boss.
Gerrard is understood to be one of the leading contenders to take charge after Barry Ferguson's interim term in charge came to an end.
Davis was put in temporary control of first-team affairs following the departure of former manager Michael Beale in October 2023.
The 40-year-old was caretaker boss for two games, a Europa League defeat by Aris Limassol and a league win over St Mirren, before Philippe Clement was appointed to the position on a permanent basis.
As a player, Davis made a total of 239 appearances for Rangers during two spells with the club.
"Steve has had the privilege and the honour of being in [at Rangers as a coach] for a little bit and I don't think it fazed him," said Northern Ireland's record men's international goalscorer Healy.
"I don't think anything ever fazed Steve as a player or as a person. He's pretty relaxed, he's pretty comfortable in his own tone and what he wants to say.
"If Rangers feel, when the new manager comes in, whoever he's going to be, feels there's an opportunity for Steve to go in. I think Steve would be an asset to have at Rangers, no matter who the manager is."
Davis is currently part of Michael O'Neill's backroom set-up with Northern Ireland, for whom he won a record 140 caps.
"I know he's going through the process at the minute where he's going to do his coaching badges," said O'Neill.
"He's going through the process of learning and, for me, there is no better role model or apprenticeship than to be working with or in and around Michael O'Neill, who is an incredibly talented coach."