The 15-year-old midfielder is widely regarded as one of the Black Cats' best youth prospects and is expected to cost the Reds around £200,000 in terms of a compensation fee.
He would likely start off in Barry Lewtas' Under-18s squad should his transfer to the Anfield club go through, though he is expected to make fast progress through to the higher ranks of the club's academy setup given his talent.
As well as looking to develop their own homegrown talent, Liverpool have looked to add a number of exciting additions to their youth ranks this summer.
England youth international Bobby Duncan was signed from Manchester City, while the Merseyside club also struck a deal for Ajax teenager Ki-Jana Hoever.
The 16-year-old full back had attracted interest from across the continent, with top European clubs scouting the player thoroughly. Chelsea, Manchester United and Manchester City were all said to be interested in the young star, but the opportunities given to young players by Jurgen Klopp reportedly convinced him of a move to Anfield.
Liverpool's Under-18s squad continued their impressive start to their season with a 2-1 win at Stoke City on Saturday, with goals from Leighton Clarkson and Tom Clayton proving enough to earn Lewtas' side the three points.
The Reds' under-18 team face Newcastle United's Under-18s in their next fixture, a potentially interesting clash for Stephenson should he have signed by then, given his Sunderland ties.