The Elland Road outfit are on the verge of kick-starting their summer transfer business with a swoop for the Premier League duo.
Harrison, who spent last season on loan with United, is set to rejoin Marcelo Bielsa's squad after undergoing a medical at Thorp Arch over the weekend.
The 22-year-old winger made 42 appearances for the club last term, bagging four goals and three assists as he helped Leeds to a third-placed finish.
White is also close to making the switch to Elland Road, with the Seagulls defender expected to complete a medical at the club ahead of a season-long loan move from the south coast.
The 21-year-old centre-back has spent time on loan with Football League sides Newport County and Peterborough United in recent seasons, and will provide Pontus Jansson and Liam Cooper with competition in the heart of defence.
Leeds remain in the hunt for one of their top summer targets in Wolves winger Helder Costa, with Bielsa's men hoping to iron out the final details on a move that will bring the 25-year-old to West Yorkshire in the coming days.
Reports over the weekend suggested the Portuguese forward had already said his goodbyes in Wolverhampton as a deal nears completion.
Elsewhere, Whites youngster Jack Clarke is poised to end a summer of speculation by completing his move to Premier League side Tottenham Hotspur after completing a medical in north London last week.
United are also close to bagging the signatures of Carlisle United winger Liam McCarron and Barcelona B forward Rafa Mujica.
The pair will head straight into Carlos Corberan's Under-23s squad, who will aim to defend their Professional Development League national title this coming campaign.