Nicola Cortese's resignation this week put pressure on the Saints manager, but the club managed to steady the ship.
Llambias resigned from his position at St James’ Park a few days after Newcastle owner Mike Ashley appointed Joe Kinnear as director of football last June and has been taking a break from the game.
But he would be willing to speak to Southampton owner Katharina Liebherr to see whether a job at St Mary’s would work for the both of them.
Les Reed, Southampton’s football development director, has stepped up temporarily to fill the breach left by Cortese’s departure but Liebherr wants to appoint an experienced chief executive or executive chairman and does not want to run the club herself.
Mauricio Pochettino has vowed to carry on with his Southampton master plan despite Nicola Cortese's departure.
The Argentinian has signalled his intention to review his position at the end of the season following Cortese's exit and the appointment of club owner Katharina Liebherr as non-executive chairman.
Asked how the boardroom changes might affect the club's long-term vision following Saturday's 2-2 Barclays Premier League draw at Sunderland, Pochettino said: "It's clear that that's a question that should be directed to the chairwoman, and it's also clear that we are just going to continue on the path we have been on.
"The club has its own procedure. Nothing has changed. We are going to carry on in the way that we have been doing, nothing is going to change in that sense. We are going to continue on the path we are on.
"I have received no news or any intention or any direction to change what we have been doing, so we are going to keep on doing what we have been doing.
"It's clear that we need to analyse many things with the chairwoman. We will see what happens in the transfer window, we also need to analyse what has happened with these two players who are injured (Jose Fonte and Gaston Ramirez).
"But overall, I can't answer so many questions in such a short period of time. I also have the same questions."