His firm was recently named Rangers official merchandising supplier and Ashley is one of the largest shareholders in the Scottish Third Division club.
Last night, Rangers chief executive Charles Green said: "We will go ahead with Sports Direct and what we're doing at the moment is getting some visuals together. We'll get those up on the website so that the fans can see what the proposals are for the stadium."
It is understood the deal will be agreed in the coming weeks.
Ashley was criticised by Newcastle United fans after he renamed the club's home ground of St James Park the Sports Direct Arena.
Green said: "We had a meeting a few weeks ago with the supporters and invited Sports Direct. We had a presentation from Derek Llambias, the chief executive of Newcastle, who spoke to about 400 Rangers supporters about how that worked for him at Newcastle.
"How that money bought Demba Ba and, after 29 goals, he sold him for £7.5m and bought Sissoko with that money.
"So, he explained that it's not just £1m then it's gone, but the important thing is that we want to get on.
"What we said at that meeting is that we'd narrowed it down to two interested parties, but one of those was not prepared to commit until he knew what league we were going to be in. We don't even know what the league is going to be called, let alone what division we're going to be playing in."
Diehard Rangers supporters have insisted Ibrox must remain part of the stadium's new title.
The move to rename Ibrox is likely to split the Light Blue fans.
Green said: "You look at it and one line says that in December we finished the year with 20-odd million pounds of cash and that begs the question, why do we need to do things as emotive as stadium naming rights?"
"But bringing an amount of cash or the branding of Murray Park is vitally impor-tant to the club.
"This is not money that goes into Charles Green's retirement fund, it goes into Rangers and we shouldn't lose sight of the fact that the team needs investment on the pitch, because it's only with a successful team that we'll get the support of the fans. That shouldn't be under-played."
Green believes the Ibrox club has made progress despite posting a loss of £7 million for the last seven months of 2012.
As reported in late editions of yesterday's Evening Times, interim results to December 31 show revenue of £9.5m, with operating expenses of £16.6m.
At the turn of the year, the club had £21.2m in the bank.
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