Newcastle owner Mike Ashley has effectively taken charge at Ibrox after his £2m emergency loan offer was accepted by the club's board.
Ashley has moved to offer Llambias a role with the Scottish Championship club and Sky Sports understands he is one of the candidates to take on the post of chief executive or managing director, depending on what the role entails.
Rangers Board Chairman Sandy Easdale spoke briefly to reporters at Ibrox on Tuesday but has only had minimal contact with Llambias.
"I've not had any discussions with him. As far as I am aware he is a consultant at the moment," said Easdale, who also confirmed he has not spoken with Ashley in the past week.
Some Rangers fans have threatened to boycott tonight's Scottish League Cup game with St Johnstone but Easdale insisted that was a matter for supporters themselves to decide upon.
"I think they need to make their own minds up. I am not going to comment on fans," he added.
"Everybody is here to do their best for the club and fans have got to realise we are working hard to achieve that."
Meanwhile, former Rangers director of football Gordon Smith has called for clarity over Ashley's future role at Ibrox.
Reports suggested Rangers were just 48 hours away from administration prior to the Sports Direct owner's offer being accepted but Smith believes a further cash injection will be required 'within months'.
Speaking to Sky Sports News HQ the former SFA chief executive said: "Rangers are in a delicate situation financially and the £2m loan is short-term as the club do need a lot of money to run forward.
"So they are going to require more money quite soon, within a few months they will be looking for more money. So does Mike Ashley come back in then?
"Does he get a shareholding at that stage or does he take over control of the club without having to buy in that way?
"I think a lot of these things need to be answered. The people who have actually given him that control and brought him in need to tell the fans out there exactly what the situation is regarding the deal that has been set with Mike Ashley."
Rangers' most recent interim accounts in March of this year showed losses of £3.5million for the final six months of 2013, with the same amount available in cash reserves.
