The 26-year-old Southampton forward had been earmarked as one of Brendan Rodgers’ primary transfer targets this summer as he aims to bolster his squad ahead of their UEFA Champions League campaign.
Southampton rejected a £20m bid from Liverpool earlier this month, but they have since returned with an improved offer for the England international.
It is understood Lallana has agreed a five-year contract with last season's Premier League runners-up.
Lallana's agent David Manasseh spoke to Sky Sports News as he left Melwood and confirmed the deal was progressing as planned.
"We're getting closer," he said. "We're nearly there on the personal terms and he's having a medical. Hopefully we'll have good news for Liverpool fans - probably tomorrow (Saturday) morning."
However, Sky sources suggest Monday is a more likely date for the deal to be completed.
The forward has made over 200 appearances for Southampton, scoring 48 goals, since joining them as a trainee from Bournemouth as a 12-year-old in 2000.
Lallana is set to become the second high-profile departure from St Mary's in the space of a few hours after left-back Luke Shaw joined Manchester United earlier on Friday.
Liverpool, who have also signed Rickie Lambert from Southampton and Emre Can from Bayer Leverkusen, have been linked with yet another south coast raid for Saints defender Dejan Lovren.
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