The Argentine comes out of contract at St Mary's Stadium next summer but Lambert feels he is the right man to lead the south coast club and has implored the Saints brass to secure him for the long-term.
Lambert also reacted positively to the re-iteration of owner Katharina Liebherr and new chairman Ralph Krueger that no key players will be sold this summer.
"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.
"The sooner we hear them things the better really.
"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.
"Obviously, he needs reassurances about going forward, about not selling our players - and not only keeping our players, but bringing in three or four players that are going to progress us again."
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