The 34-year-old has established himself as the Ibrox No.1 following Allan McGregor's summer exit.
And he is desperate to extend his five-year stay at the Light Blues when his current contract expires next summer.
Alexander is determined to help play a key role in taking Gers back up through the divisions.
But the keeper, who was one of string of top team stars who agreed to a 75% wage cut when the Ibrox club entered administration back in February, reckons he has earned his new deal as much through form as loyalty.
He said: "My contract is up in the summer. The club have come out and said they want to repay the loyalty and obviously Lee McCulloch has signed a new deal and that is fantastic.
"I think they have made contact with my agent and they are talking. Hopefully we can get something sorted out as I have never hidden the fact I want to stay with Rangers.
"I like to think that not just five or six months, but that in the last five years I have done well here and I deserve a new contract with Rangers.
"And not just for the loyalty I have shown in taking the 75% cut, but because I deserve it on my form.
"I would love to play a part in helping to take Rangers back where they should be and this is just the first step. I want to stay longer and help us get back to the SPL.
"So hopefully my loyalty will be rewarded in that respect and I will get the opportunity to do all that."
Alexander has also hailed the return of former manager Walter Smith as non-executive director and backed the job being done by chief executive Charles Green.
He said: "It is fantastic Walter is coming back to the club. I regard him as the best manager I have ever worked under and I think it is a great thing for the club.
"I think Charles Green is doing a fantastic job and is the right man to take the club where it needs to be.
"To get Walter back is a really fantastic thing for the club in whatever capacity he is back in. He has tremendous knowledge and experience and that can benefit the club massively. He cares so much about Rangers it can only be a huge plus to have him back."
Turning his attention to this afternoon's trip to face East Stirling, Alexander says he won't be unsettled by the artificial surface at Ochilview.
He said: "Obviously it is not an ideal surface for diving or kicking on. Your knees, your hips and your elbows all take a bit of a battering and it takes longer to recover after.
"But once that whistle has gone, you just get on with it and do what you do. Goalkeeping is an instinctive thing and you just get on with it and cope with it.
"We know we will get a test at Ochilview."
Meanwhile, Carlos Bocanegra – on loan to Racing Santander – is facing six weeks on the sidelines after tearing a hamstring playing for the US against Russia in midweek.