Murray last week gave McLeish until the start of December to turn around a disappointing start to the season.
But that was followed by a 3-0 defeat by SPL leaders Celtic that left the reigning champions 15 points adrift in the Scottish Premier League.
McLeish could save Rangers' season - and his own job - with victory in Portugal as the Glasgow club attempt to qualify from the group stages of the Champions League.
But Murray has made it clear that he is making contingency plans and Le Guen emerged as his favoured option ahead of the much-touted Charlton Athletic manager, Alan Curbishley.
I cannot say that he will not be the next manager of Rangers
Agent Frederic Guerra
Le Guen admitted on French television that he knew Rangers were looking for a coach but would not be drawn further on the matter.
Agent Frederic Guerra said: "I cannot say anything. Like doctors, we have professional confidentiality.
"I cannot say that he will not be the next manager of Rangers, but neither can I say that he will be the next manager of Rangers.
"The situation at the moment is Paul now works for television, but who knows what is around the corner?
"He wants to return to coaching, but I cannot say when at this moment in time.
"It is also possible he could return to coaching in Scotland, but there are many possibilities.
"He could go to Rangers, Locomotiv Moscow or elsewhere. I just don't know."
The 44-year-old Le Guen, who guided Lyon to three straight titles, has rejected several offers from clubs around Europe, saying he intends remaining a French television football pundit until the end of the season.
He had quit as Lyon coach in Lyon in May, despite having been offered a three-year contract extension.
Le Guen previously coached Stade Rennes between 1998 and 2001, joining Lyon after the club had claimed the first title in their history in 2002.
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