The up-and-coming English midfielder is also watched by other clubs that include Derby County, Sheffield United and Brighton.
However, Bristol are demanding £15million for the suitors to get the signature of Brownhill.
Brownhill’s impressive season with Bristol
The 23-year-old has had an impressive season with Bristol, garnering a nine-goal tally in 45 appearances.
Furthermore, he has been at the heart of the midfield for the Robins in the past two seasons, making a total of 132 appearances.
His notable moment with the Robins was when he scored the decisive goal to defeat Premier League side Huddersfield Town in the FA Cup.
The former Manchester United youth product commenced his career with Preston North End and had a loan spell in between at Barnsley.
A central midfielder by tradition, Brownhill can also occupy several positions in the middle of the park.
Should Leeds consider a move for Brownhill?
Leeds have an array of midfield options at the moment, yet the form of Adam Forshaw will be a concern for Bielsa.
The 27-year-old was rather used as a substitute and failed to make an impact throughout this campaign. And the Argentine manager can seek the services of a player like Brownhill to bolster their squad for the upcoming season.
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The Robins’ midfielder can also form a daunting partnership with Mateusz Klich and Kalvin Phillips should he opt to move to Elland Road.