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...
9. Joao Pedro - A
Brighton are close to sealing a £30m deal for the Brazilian attacker from Watford. De Zerbi described him as a 'great player' and he will add to his options. Can see him playing just behind Ferguson Photo: Nigel Roddis
10. Kaoru Mitoma - LW
One of the most dangerous players in the Premier League at the moment. De Zerbi hinted the Japan international will still be at the Amex next season, despite plenty of interest Photo: Mike Hewitt
11. Evan Ferguson - A
Has the potential to Brighton's main man in attack next season. Ferguson has all the tools to be one of the best strikers in the Premier League Photo: GLYN KIRK