Birmingham midfielder Charlee Adams has signed a new one-year contract with the club.
Southampton are confident Jay Rodriguez will commit to a new long-term deal but the player will consider his options.
Bill Miller has promised to end the culture of overspending at Rangers after being confirmed as the preferred bidder by the club's administrators.
Miller is seeking to buy the assets of the club, which could have debts of up to £135million, and form a new company while bidding to take the current club out of administration.
The club were forced into administration in February over unpaid VAT and PAYE bills accrued since the takeover of Craig Whyte a year ago.
Whyte completed his deal by paying off the club's £18million bank debt with money sourced against future season ticket sales after buying the 85% stake of Sir David Murray.
Murray had previously underwritten a £50million share issue scheme after debts reached more than £80million.
The club could face a further tax bill of up to £75million over the use of employee benefit trusts for a decade.
Miller released a statement through the club which described his opportunity to buy "one of the UK's most venerable football clubs" as a "great honour and privilege".
The American added: "What Rangers, which includes supporters, players, staff and anyone with the club at heart, have been put through, particularly in recent months, is a travesty and from what I can see they have been badly let down by a number of individuals.
"This will not happen on my watch should I become the custodian of this great club.
"Under my stewardship, Rangers will be managed with fiscal discipline such that the club not only conforms to UEFA financial fair play regulations but also such that Rangers will never have to suffer this kind of anguish again.
"From now on, Rangers will live within its means - no excuses."
Miller's £11.2million plans have been criticised by some fans who fear the end of the club formed in 1872.
The towing-truck tycoon's plans involve merging his new company with the old company at a later date, but that would involve agreeing a Company Voluntary Arrangement and possibly dealing with Whyte.
But the 65-year-old has pleaded with fans to support his plans and insists the history will remain intact.
"I have fought hard to try and offer Rangers a fresh start and I hope all Rangers fans will continue to rally round the club as we endeavour to leave behind this distressing chapter in the club's history," he said.
"Finally, and perhaps most importantly, we have worked hard to ensure that there is no loss of history, no loss of tradition and no liquidation of Rangers Football Club.
"I wouldn't have it any other way."Former Rangers player Sandy Jardine, who has played a central role in mobilising supporters' action in recent months, urged fans to back Miller.
Jardine, who works for Rangers, told the club website on Thursday: "I spoke to Bill at length this afternoon and took great comfort from what he had to say.
"I told him our supporters want honesty and transparency and I was impressed with what I was told.
"He wants to get Rangers Football Club back to good health and is eager for fans to have fun and enjoy their football.
"I know he is working extremely hard behind the scenes to conclude a deal as he wants to make the club work.
"Our supporters don't know a lot about him but I was delighted with what he told me and he is clearly determined to get the club back on track.
"Bill has also spoken to Ally McCoist today and outlined his plans to fix Rangers.
"I would encourage all supporters to get behind him and unite as he is stepping up and doing all he can to save our club and preserve its history.
"His plan does not involve liquidation, there is no doubt about that and I have to say I was left feeling very positive after our conversation."
However, Rangers Supporters Assembly spokesman Ross Blyth tempered his excitement after being let down by Whyte's promises last year.
Blyth told Sky Sports News: "We don't know enough about Bill Miller at the moment.
"If he keeps his promises it would be a fantastic deal for the club. It keeps the history of the club, without liquidation, so it could be great.
"There is still a good bit of work to be done. We're pretty excited by it but we realise there is a long way to go."
Blyth admitted fans were naturally sceptical over the American's motives.
"As we go back to this time last year we were excited," he said.
"We had just won the 54th title and Craig Whyte came in, supposedly the knight in shining armour, with promises of £5million a year in the transfer pot.
"He broke all his promises so the fans are a bit damaged by this over the last year.
"If it's the same type of scenario we sit back and have a few more questions this year.
"There is a little bit more to know about this guy before we get behind him."