Teamtalk reported that both Sheffield United and Burnley were making late pushes to sign the Bristol City star ahead of the August transfer deadline - with the Blades manager, Chris Wilder, in particular, said to be a long-term admirer.
And the website claimed that the Robins would have demanded a fee in excess of £15 million for Brownhill, who has scored or assisted six goals in 19 games for the Championship's fifth-placed side this season.
But asked how he will respond when the 'inevitable' happens and an approach does arrive, Ashton told the Bristol Post. "The message is really simple and that goes for all the players, we do not have to sell anybody and that’s where I am so fortunate, that Steve and Maggie (Lansdown, the Bristol City owners) are outstanding.
"I’ve been here when it was Jonathan Kodjia, Bobby Reid, Aden Flint, Webby (Adam Webster); they have never once said to me, go and get as much as you can."
"It’s been the other way around: part of the business development is, "Steve, this is happening with player X, we may get an offer in with player Y, if I think it’s the right offer I will bring it to you to get your thoughts and the board's."
"There’s never been a fallout with me, Lee, the Lansdowns on any player either incoming or outgoing at this football club and the reason for that is that the communication is so good and that’s the piece and as long as everybody is honest with the communication, you’re never going to go too far wrong."
Brownhill is under contract at Bristol City until 2021 - although it is thought that his deal may contain a 12-month extension option.
But a move back north with either Sheffield United or Burnley - who remain in the hunt for European qualification - could appeal to the Warrington native after three-and-a-half years away.
Sheffield United and Burnley fans - would Brownhill be a good addition for your side?
Have something to tell us about this article?