Milner, 37, is out of contract with Jurgen Klopp's team this summer and will be available on a free transfer.
Brighton are keen to add experience to their youthful and talented squad and see the former Leeds, Newcastle, Aston Villa and Man City man as the perfect fit.
It is thought Milner, who has 61 England caps to his name, is impressed with the project at Brighton and likes the style of their head coach Roberto De Zerbi.
The Italian has worked well with his veteran players such as Adam Lallana, Lewis Dunk and Danny Welbeck – and Milner could have a similar positive influence on the squad on and off the pitch. Milner can play anywhere across the midfield and also at right back and has made 38 appearances for the Reds this season and 225 in total since arriving at Anfield from City in 2015 for £26m.
Here's how he could fit in Roberto De Zerbi's Brighton starting XI for next season...
5. Pervis Estupinan - LB
The left back has enjoyed an excellent first season in the Premier League having replaced Marc Cucurella, who moved to Chelsea Photo: Mike Hewitt
6. Pascal Gross - CM
The experienced German has been undroppable this season and he will be vital next term as Mac Allister and Caicedo are expected to exit Photo: Mike Hewitt
7. Solly March - M
A slightly deeper role is on the cards for March next season as De Zerbi looks to accommodate some flying new attackers Photo: Charlie Crowhurst
8. Simon Adingra - RW
The Ivorian has been excellent for Union SG this season and will look to make an impact - similar to Mitoma - in the PL next season Photo: KURT DESPLENTER