A figure of £4million plus add-ons is the anticipated fee that both clubs have agreed.
The former Bristol Rovers, Stockport and Rochdale forward scored 14 goals in 39 games for Saints last season.
If everything goes to plan Lambert will travel to Merseyside after England's friendly with Peru at Wembley on Friday night and could be confirmed a Liverpool player as early as Monday.
It is reported that personal terms have already been agreed between Lambert and his prospective new employers.
TWEET: Rickie Lambert made 10 assists in the Premier League last season. The only Englishman to register more was Steven Gerrard (13).
Lallana was seen as the primary target to bolster the Reds' midfield, with Lovren less so for the centre of defence, but Lambert looks like being the first through the door at Anfield in what is expected to be a busy summer as they look to strengthen ahead of a return to the Champions League.
Liverpool have made a bid, reported to be in the region of B£16million, for Sevilla left-back Alberto Moreno but are still in negotiations with the Europa League winners.
Press Association Sport understands further talks with Bayer Leverkusen midfielder Emre Can over the weekend are likely to give a clearer idea of whether the Germany Under-21 international will also move to Merseyside.
Although there is a buy-out clause of about B£10million which Liverpool are willing to meet, the player's wage demands are proving a significant stumbling block.
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- Bristol Rovers
- Adam Lallana