Graeme Murty is "desperate" to become Rangers manager on a permanent basis despite it being understood that Steven Gerrard is a contender to take over.
Sky Sports News believes the Liverpool academy coach and former England captain has held initial talks with the Ibrox hierarchy.
But Murty, who took over in October as interim boss until the end of the season, wants to build on his achievements with the team second in the league.
Speaking ahead of Sunday's game against Celtic which could see Brendan Rodgers' side win a seventh consecutive Scottish Premiership title, the 43-year-old said: "I'm in the role, I love the role, I will do everything I possibly can to keep the role.
"I will be fighting as hard as I can in these last four games to finish as high up the table as I possibly can and do my job to the best of my ability.
April 29, 2018, 11:30am
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"I think I've done a good job so far. We've gone from fourth to second with a squad of players that aren't mine, with a style of football that's starting to look how I want it to, and I am desperate for the opportunity to bring my own players in and bring my own stamp on the team."
Murty was asked if he thought the board were aware of his enthusiasm to stay put. "They know that," he added. "There has never been any doubt about that. I am marvellously honoured to be sitting here.
"People would love this job, trust me it's a massive job, it's a stellar job and I'm desperate to hold onto it. I think I've done a really good job so far and I want a chance to continue."
Murty's hopes of staying at Ibrox long-term were dealt a blow when his team were comprehensively beaten 4-0 by Celtic in the Scottish Cup semi-final, and he accepts they have to do better.
"There is another opportunity on Sunday for the players that played last time to go and show themselves in a better light," he added.
"If there is a new manager to come in at the end of the season which there will be, they [the players] are all auditioning so what they need to do is make sure they perform properly.
"If it is not to be me then someone else will have a fantastic job but I reiterate that we have to go and make sure we focus on Sunday because that's all we can control.
"We can only control ourselves and what we do on the pitch."
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