The Ibrox outfit are looking to fill the role following the resignation of Graham Wallace.
The news comes as Rangers confirmed the agreement of an emergency interest free £2m loan from Newcastle owner Mike Ashley.
Llambias will fly into Glasgow over the next 24 hours for talks.
Wallace quit his role on Monday morning, and he follows finance director Philip Nash in leaving the club.
Ashley, whose loan is secured against Edmiston House and the Albion car park, had wanted Wallace and Nash to leave the club.
The Newcastle owner will now "put forward" two names to be elected to the Ibrox board.
Wallace was appointed Rangers chief executive in November 2013.
Ashley - who owns 8.92% of the Championship side - saw off rival offers of funding from former Rangers director Dave King and Sale Sharks owner Brian Kennedy.
"The board is pleased to announce that the company's subsidiary, The Rangers Football Club Limited, has entered into a credit facility agreement with MASH Holdings Limited pursuant to which MASH shall make available the sum of £2m for drawdown by the company," a Rangers statement to the Stock Exchange read.
"MASH is a shareholder in the company holding 8.92 per cent of the voting rights in the company. The facility shall be secured by standard security granted by the company over Edmiston House and Albion car park.
"The facility shall be for a six-month term and is interest-free. The facility will be used by the company for general working capital purposes. Under the terms of the facility, MASH has the right to appoint up to two directors on the board of directors of RFCL."