The 32-year-old left the club in the summer after six years.
He played 178 games and scored 22 goals during his spell at the club.
Lallana won a Premier League medal last term, and was on the bench during their 2019 Champions League, UEFA Super Cup and FIFA Club World Cup successes.
When he left, manager Jurgen Klopp described him as a legend and "one of the most influential players I've ever had in my life on the training field."
The Brighton & Hove Independent quotes Lallana as saying in response: "It's a great compliment, but I am not comfortable talking about myself and using that word, there are far more legends associated with that football club.
"We had such a strong squad at Liverpool and a really tight core – I was a big part in Jurgen's five years at the club.
"It was nice to be part of that environment and see the journey he took the club on to win the league."