According to Teamtalk the trio - along with Burnley, Bournemouth and Leicester, all of whom were credited with interest by the Sun in August - are keen on signing Brownhill, whose Robins contract expires at the end of this season.
The 21-year-old has played an integral role in Bristol City's march to third place this season, scoring three goals and creating one more in the Championship.
And though the Robins do have an option to extend Brownhill's deal by a further 12-months, Teamtalk reports they are desperate to extend his stay beyond that amid interest from the likes of Newcastle, Leeds and Derby.
Newcastle's failure to get their proposed takeover across the line is likely to leave them on the lookout for bargains in January, and Brownhill's situation means he could tick that particular box.
He is not the only Championship midfielder to be linking with a move to promotion chasing Leeds and Derby this week, after his namesake and fellow Lancastrian Josh Vela at Bolton [Daily Mail].
Would Brownhill be a good signing for Newcastle/Leeds/Derby?