The Reds’ £4m offer plus add-ons has been accepted by the south-coast club, with Lambert set to sign a two-year deal after undergoing a medical tomorrow.
Lambert is just the first of a trio of signings Liverpool hope to make from St Mary’s.
Brendan Rodgers also wants England midfielder Adam Lallana and centre-back Dejan Lovren as he bids to capitalise on the uncertainty at the club following manager Mauricio Pochettino’s move to Tottenham.
Liverpool have had a £20m offer for Lallana rejected already, with Southampton wanting £30m.
Talks have stalled because of a 25 per cent sell-on fee the Saints will owe Bournemouth should Lallana be sold.
Liverpool have lined up £15m Bayern Munich star Xherdan Shaqiri as an alternative to Lallana, but rumours indicate a triple move could be worked out for all three Southampton players to head to Anfield.
Internet message forums have been flooded with claims that Lambert, Lallana and Lovren are on their way to Merseyside in a convoluted package deal.
The theory suggests Liverpool will pay a lesser fee for Lallana in order to save Southampton paying out 25 per cent of it to Bournemouth.
That money would be recouped in the transfer fees for Lambert and Lovren.
While any such move is clouded in mystery, it appears likely that the England striker will complete his move in the coming days.