The 21-year-old midfielder is out of contract at the end of the season and attracting attention from a variety of golfing apparatus.
According to TeamTalk, there’s Premier League interest from Newcastle, Leicester, Bournemouth and Burnley.
Championship play-off hopefuls Derby are also prepared.
Brownhill is in talks with City over a brand spanking new contract.
He has an selection for an extra 12 months on the other hand Robins chiefs are determined to tie him proper right down to a longer-term deal.
The Warrington-born ace moved to Ashton Gate upon the expiry of his Preston contract in 2016.
He has made 54 appearances for the club, appearing 22 circumstances this period of time in all competitions this period of time.
City are third throughout the Championship table and would most definitely be reluctant to advertise.
Brownhill has previously indicated he’s satisfied at the club.
When asked in September if he has a long-term long term at Ashton Gate, he said: “Yeah, this is a great club and an excellent fan base and great manager and if everything is in the correct place you need to amplify as a player and keep taking part in.
“So I don’t see why no longer. I like the membership, love the fanatics and as I say I consider what the executive has to provide and the way in which he performs soccer.”