The 23-year-old has been a regular in the Norwich squad since the 2018/19 season, being one of the standout performers in the team, despite the struggles that the Canaries have faced in the top-flight.
Cantwell was involved in eight goals during the 2019/20 Premier League campaign, becoming one of the club's most important players even though they were relegated.
Cantwell managed six goals and six assists last season in the Championship, as Norwich propelled themselves back up to the Premier League.
Leeds were linked with a move for Cantwell during the summer transfer window, with Leeds Live citing Sky Sports reporter Dharmesh Sheth who stated that the midfielder was valued at around £40 million ahead of the 2021/22 season.
Sheth said that "it would take a significant offer for Norwich to even consider a sale for Cantwell in this transfer window", adding that he has "heard figures upward of £40 and £50 million before Norwich could consider a sale of Cantwell".
Leeds Live are now reporting that the Marcelo Bielsa's team is now pushing for a 'cut-price' deal for Cantwell, mainly due to his contract with Norwich expiring at the end of the season.
With Raphinha's future at the club being in doubt due to plenty of interest from top Premier League clubs, Cantwell has emerged as a contender to take his place, especially with the English midfielder's energy that would fit in with Bielsa's style.
Cantwell has played in five games so far this season, finding it hard to nail down a spot in the side after Norwich's disappointing start to the season.