Lewis-Potter has left Hull's pre-season trip to Turkey to thrash out personal terms with the Bees.
The 21-year-old, who has made four caps for England Under-21s, came through the Hull academy, before breaking into the first-team in the 2019/20 season.
The forward became a regular with the Tigers after their relegation to League One a season later, where he scored 13 goals to help them to immediate promotion back to the Championship.
Lewis-Potter then netted 12 times in the second tier last season, which attracted interest from the likes of Brentford, West Ham United, Everton, Southampton and Nottingham Forest.
Thomas Frank will be hoping the forward can replicate what another ex-Hull man, Jarrod Bowen, has done at fellow London club West Ham.
Bowen and Lewis-Potter briefly played together during their time at the KC Stadium, and the latter will be hoping to settle into the top-flight as well as the now-England international did.
The West Ham man has scored 20 league goals over the last two seasons and has been linked with a move to Liverpool.
The west Londoners are looking for more creativity after the departure of Christian Eriksen, who is set to sign for Manchester United on a free transfer.
The midfielder joined the Bees on a six-month contract in January, helping the newly-promoted side avoid relegation.
Brentford's only signing of the summer so far was Scottish full-back Aaron Hickey, who they signed from Serie A side Bologna in a club-record deal.
But they are now set to break that record again with the signing of Lewis-Potter.