Bull is known to be a big hit with Johnson, who has said he will bring in at least one goalkeeper to Ashton Gate this summer after transfer-listing his former number one Steve Phillips this week.
Johnson was believed to be interested in signing Bull while manager at Yeovil and talk in the west country is that he could be ready to pounce again.
Bull still has two seasons left on his Shots contract but any interest shown by Johnson and City would be very hard for him, or the financial state of the club, to ignore.
Still only 24, Bull has arguably become one of the hottest properties in the Conference during his three years at the Rec, but his frustration at having conceded the most goals last season was clear to see.
If Bull was to sign up at next season's pre-season favourites for League One, he would go head-to-head with former Woking keeper Adriano Basso for the number one jersey — a challenge he would no doubt relish.
Brown, however, played down the speculation, saying: "Hand on heart, this is the first I have heard of this.
"Nikki is my club captain and certainly not somebody I'll be looking to let go this summer."
With thanks to the Aldershot News.