The Saints manager has just over a year remaining on his current deal but Lambert believes that the club would benefit from moving quickly to ensure that the Argentine is not targeted by other teams.
"I think it's important that you hear the things you want to hear – that players are not going to get sold, that we're going to be trying to push on again next year and progress the way we've been progressing the last few years," Lambert told the Daily Echo. "Obviously, having the gaffer here, I think that's the main thing – getting him tied down to a contract.
"Obviously, we're focused on our jobs fully, but I think, not just for the players but for the whole club, the quicker the manager gets tied down to a contract the better for everyone."
Southampton are currently eighth in the Premier League.