The clubs are in talks over a deal for the England Under-21 international, the PA news agency understands.
A fee of £15million has been reported but no agreement has been struck and the midfielder still needs to agree personal terms at Elland Road.
Leeds boss Marcelo Bielsa refused to confirm the approach.
Speaking after his side’s win over Sheffield United, Bielsa told BT Sport: “We only like to talk about signings when they are actually made because a lot can happen during these moments. So I don’t like to talk about signings until they are confirmed.”
Cantwell was left out of Norwich’s squad for their Sky Bet Championship trip to Bournemouth on Sunday.
Leeds have already spent a club record £30million on striker Rodrigo from Valencia and signed defender Diego Llorente from Real Sociedad for a reported £17million, having lost out on Josko Gvardiol to RB Leipzig.
The Norfolk-born Cantwell has come through the club’s academy and has scored eight goals in 70 appearances.
The 22-year-old impressed last season despite the Canaries finishing bottom of the Premier League, scoring six times in 37 games.
Cantwell is expected to be the Canaries’ last major exit this window, unless a huge bid comes in for one of their stars.
Norwich sold Jamal Lewis for an initial £15million to Newcastle earlier this month.
Emi Buendia, who was keen on returning to the Premier League, is now likely to stay at Carrow Road if Cantwell completes his move.
Max Aarons has been wanted by Barcelona while Roma and AC Milan have also been linked with the right-back and defender Ben Godfrey still could stay.
Striker Teemu Pukki is expected to remain at Carrow Road despite having interested Wolves, Leeds, Sheffield United, Aston Villa and West Brom this summer.
Moritz Leitner, Josip Drmic and Tom Trybull are all free to find new clubs after they were stripped of their squad numbers, with midfielder Leitner in talks with three Championship clubs as well as some in Europe.
