Ashworth is an admirer of the Liverpool and former Southampton midfielder and has been working on the deal since January.
Lallana is expected to sign a three-year contract at Albion early next week, which is reportedly a longer deal than other clubs also targeting the 32-year-old were prepared to offer.
Leicester City, Everton, Leeds and Burnley were all said to be keen.
The former England player is out of contract and departing Liverpool after 178 appearances in which he contributed 22 goals and 22 assists following his £25 million move from St Mary’s in 2014.
During his time on Merseyside, Lallana won the Champions League, the Premier League, the Uefa Super Cup and the Fifa Club World Cup.
Brighton are keen to add experience to their squad having secured their Premier League status for a fourth consecutive season last Monday thanks to a 0-0 draw against Newcastle.
It would be seen as quite the coup for Albion to acquire a Premier League and Champions League winner, who helped set the standards required of the Jurgen Klopp era at Liverpool.
Both Klopp and Liverpool captain Jordan Henderson credited the England international with helping the club back to the very top of the game.
Lallana's know-how both on and off pitch would be an asset on the south coast and they view him as a perfect role model for their younger players such as Steven Alzate, Alexis Mac Allister, Aaron Connolly and Tariq Lamptey.
He arrives as a free agent but his wages could be as high as £90,000 per week, which would comfortably make Lallana the highest paid player in the club's 119-year history.
There are concerns however that the high salary could disrupt the wage structure in place at Albion and also if that represents good value for a 32-year-old with a history of injury problems.
“There are parts of me that are excited about my next challenge,” said Lallana who won the last of his 34 England caps against Italy in March 2018.
“I’m close to knowing what’s happening so there’s a mixture of emotions really at the moment.
“It’s unfortunate I won’t get a chance to properly say goodbye (to the fans), but I’m pretty sure I’ll be back at Anfield and hunting for three points against them.
“I’m sure they’ll give me a nice welcome and it’ll be nice to say goodbye properly and I’m sure that will happen next season at some point.
"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."
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