The Reds had a bid accepted for the 32-year-old and Sky Sports News understands personal terms have been agreed.
Lambert, who was born in Kirkby, was part of the youth team at Anfield before being released at 15 and is a lifelong Liverpool fan.
Southampton legend and Sky Sports expert Matt Le Tissier tweeted: "If Rickie joins lfc I will say good luck to him and thanks for helping to resurrect #sfc it's his boyhood team and in CL.#stillahero."
The centre-forward, who is in England's squad for this summer's World Cup, scored 14 times last season for the Saints, who paid Bristol Rovers £1m for the player's services in August 2009.
Since then he has become an established Premier League striker and scored on his England debut, notching with his first touch in international football after coming on as a substitute against Scotland in August 2013.
A powerful and strong player, Lambert is also a free-kick specialist and has an exceptional penalty record, having scored his past 34 spot-kicks and having never missed for Southampton.
He has played in all four divisions of the Football League and his story is one of resilience, having endured limited success at Blackpool and Macclesfield Town before improving considerably at Rochdale and Rovers.
Lambert's career took off at the Saints, for whom he scored 117 goals in 235 appearances and won two promotions, producing the kind of form that brought him international football and interest from Champions League club Liverpool.
The Reds could unveil Lambert as early as Monday.
And Ian Rush believes Liverpool boss Brendan Rodgers will be looking to reinforce 'every department' of their squad in the summer transfer window.
The Liverpool goalscoring great told Sky Sports: "With the Champions League, I am sure they will be looking at every department to strengthen.
"What do you do if Luis Suarez or Daniel Sturridge gets injured?
"It also depends on who is available at what price. I am sure Brendan will be looking at every angle.
"Brendan will have his people in mind. They scored more than 100 goals and had a fantastic season but let a lot of goals in.
"Defensively, they have got to be looking to try and stop those goals going in. I am sure Brendan will be looking at a lot of set-pieces where they lost goals.
"I think, defensively, maybe they will be looking to strengthen and maybe in midfield, as well.
"When you look at the goals scored, more than 100 goals, you cannot fault them for much."
Rodgers said on Thursday that he does not envisage signing any players on loan again this summer.
Since taking charge at Anfield, Rodgers has regularly dipped into the loan market to bolster his squad, with the likes of Nuri Sahin, Victor Moses and Aly Cissokho all spending time on Merseyside.
But now, with a UEFA Champions League campaign on the horizon, Rodgers does not believe loan signings will be beneficial to his squad.
"I would hope we don't have to go for loans this summer," Rodgers told the Liverpool Echo.
"But it's always about the availability of players. If you are not satisfied with the squad and you feel you can improve it, then you have to look at every option.
"In these first couple of years I've been here, we have had to do that as we've had a thin squad.
"The players we wanted we couldn't get but we're hopeful that this summer will be different. We turn the page and it's another chapter in terms of where we are going.
"Hopefully that will mean it will be more permanent players than loan players but I can never rule it out completely. There could be a situation where a player becomes available, we can get him and he can add to what we're doing."