Lallana, 32, is out of contract at Liverpool but is leaving the club as a Premier League champion.
According to The Athletic, Lallana has accepted a cut to his £100,000-a-week wages to join up with Graham Potter’s side.
Brighton will also give Lallana the chance to take on a coaching role when he hangs up the boots.
Lallana moved to Liverpool from Southampton in a £25m deal back in 2014.
Although a regular starter for his first few seasons, Lallana has had to settle for a reduced role in recent years.
The England international started three league games and appeared as a substitute 12 times for title-winners Liverpool this term.
An announcement on his move to Brighton is expected in the next few days.
Lallana yesterday took to Instagram to thank Liverpool fans for their years of support.
View this post on Instagram
Nothing but love and appreciation for the last 6 years. Thanks to the amazing people who made this place feel like home. To the supporters for accepting me and making me feel like one of their own. The staff – the world-class staff – without whom none of what we achieve as players would be possible. I can’t find the words to do justice for how much they mean to me… they are everything! To Brendan Rodgers, I will forever be grateful that he gave me the privilege to represent this club. To Jürgen Klopp, an even better man than he is a football manager. My teammates, they are my brothers. To share this journey with these boys has made me feel the luckiest fella in the game. To the Skip, Jordan Henderson… my best friend! No one deserves success more than this guy. It’s meant everything to be at his side while he’s achieved it. And to my own family, my wife and children, my mum, dad and sister… my own “team”. They made the good times better and the tough times bearable. I am so grateful to have been part of this special place. And now on to the next adventure. With love, Adam