The Argentine’s current deal runs until the end of next season, but there is already some uncertainty about his future beyond this summer.
Neither chairman Ralph Krueger nor Pochettino himself would be drawn on whether negotiations had begun, when asked about the issue over the course of the last week.
While Lambert was pleased to see a new board of directors put in place at St Mary’s, two months after the departure of previous chairman Nicola Cortese, he said it is crucial they move quickly to get the manager to sign an updated deal.
“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,” he said.
“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.”
Pochettino, who has been linked with Saints’ next opponents, Tottenham, said last week that it is not a priority to discuss a new contract.
However, Lambert confirmed it is something he would like to see agreed before the season’s end, in order to avoid an unsettling summer.
“I think so. I’m not going to try and play it down,” he said.
“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.”
Lambert believes that “the sky is the limit” when it comes to Pochettino’s potential, and it is increasingly clear that his future presence at the club could have significant bearing on Saints’ ability to retain their best players.
“I think it’s early in his managerial career. I know he’s managed for a few years, but I think his potential is the sky really,” said Lambert.
“I think we can see that, and I think everyone else can see that, so it’s important that we get him tied down.
“I think once the gaffer’s signed then I think that’s going to reassure everyone and that will give everyone else confidence of the direction we’re going to go.”