Liverpool would like Lambert to complete a medical on Saturday before travelling to the United States with the England squad the next day, according to the BBC.
Sources told ESPNFC.com that Lambert has been aware of the interest from the Anfield for several days, with the Liverpool-born striker eager to complete what would be a dream move to Merseyside as he looks to complete his journey from the bottom of the English football pyramid to the Champions League.
Lambert spent time at the Liverpool academy in his youth but was released by the club and played for Blackpool, Macclesfield Town, Stockport, Rochdale and Bristol Rovers before he was signed by Alan Pardew at Southampton in 2009.
Pardew made public declarations that Lambert needed to work on his fitness and technique to realise his potential, and the striker exploded into life in League One, scoring 30 goals in his first season at St Mary's Stadium and 21 goals in the 2010-11 promotion winning season that followed.
Another 27 Lambert goals in the Championship helped Southampton to another promotion in the 2011-12 season, and he has scored 28 goals in his first two campaigns as a Premier League player.
That form saw the 32-year-old rewarded with a place in England's World Cup squad for this summer's finals in Brazil, with Lambert now looking set to complete a fairy tale return to Liverpool ahead of the start of the next Premier League season.
Some will be surprised by the move from Liverpool manager Brendan Rodgers to sign the target man after he swiftly off-loaded towering striker Andy Carroll following his appointment as Reds boss in the summer of 2012, but it seems as if he has always been a fan of his first summer transfer target.
"I think Rickie is a terrific player," the Liverpool manager said of Lambert last year. "People look back now and say it was a mistake to let him go but there may have been something that was a factor.
"Rickie may not have been interested in football at the time or there may have been something else in his life. He just might not have been ready for what Liverpool was about at that time but there is absolutely no doubt within development that it cannot just be about what the player is now."
Lambert's imminent departure will fuel the fear among Southampton supporters that a summer exodus beckons from Southampton following manager Mauricio Pochettino's decision to join Tottenham last Monday.
England World Cup stars Luke Shaw and Adam Lallana are also being linked with big money moves to Manchester United and Liverpool respectively, with sources telling ESPNFC.com that Shaw's move to Old Trafford is still on course despite recent reports suggesting Chelsea are preparing to hijack the deal.