The 37-year-old will be a free agent when his Liverpool contract expires at the end of the season and will leave Anfield after eight glittering years on Merseyside.
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Milner signed for Liverpool 2015 after running his deal down at Manchester City.
He has racked up 328 appearances for Jurgen Klopp's side - banging in 26 goals - the most he has scored at a single club.
During his time at Liverpool, Milner has won the Premier League, FA Cup, Carabao Cup, Champions League, UEFA Super Cup, Community Shield and the Club World Cup.
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Despite entering the twilight of his career, the 61-cap England international has still featured in 37 games in all competitions this season.
Jurgen Klopp is a huge admirer of the ex-Aston Villa man, and was understood to be keen on extending his stay beyond the summer.
But Brighton have made a move and Milner is keen on a new challenge and the prospect of more starting time as he approaches the end of his career.
Former Liverpool teammate Adam Lallana is understood to have played a role in convincing him to join the Seagulls.
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Brighton have had an outstanding season and beat Man United in dramatic circumstances on Thursday night, to remain firmly in hunt for European qualification.
They are not resting on their laurels and are acting fast in securing their summer targets, with talkSPORT revealing recently that they had agreed a club-record deal with Watford for Brazilian forward Joao Pedro.
The 21-year-old has been with the Hornets since January 2020, but is now set to move on after two-and-a-half seasons for a fee of around £30million.
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Pedro, Watford's top scorer with 11 goals in 35 Championship games this term, is set to formally complete his move once the transfer window opens in June.
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