The Southend boss refused to give any real comment on a potential move.
It has been a tough season if you are a Bolton Wanderers fan. The club are in a potentially disastrous financial position and results on the pitch have therefore been negatively impacted as a consequence.
Former Bolton striker Dean Holdsworth has however led a buy-out of the club with his own consortium with the hope of turning things around for the club.
It was also reported that Holdsworth would be making moves to bring in a new manager to replace current boss Neil Lennon.
The Southend United manager has worked wonders in the lower leagues and Bolton's new ownership were said to be keen on bringing him in.
The Shrimpers boss was on Sky Sports News this morning (02/03/2016) and he was asked about the links. He remained respectful of current boss Lennon and decided not to make any pressing comment.
"My association with Bolton goes back 15-20 years as a player, as a coach, as a manager.
"It was inevitable I think that if I did a half decent job at Southend in the lower divisions and got us to where we are that there would be speculation.
"Sam Allardyce asked me to join him at Sunderland, the club I supported as a kid. Now all the speculation about Bolton Wanderers.
"They've been in financial disarray truth be known for the last two or three years and now that is coming to fruition.
"It's really difficult for me to talk about it when there is a man as good as what Neil Lennon in the position at the moment. So really it is not right for me to say. I wish 'Lenny' good luck from now until the end of the season."
It was good tact from Brown not to make much comment on Lennon, who has struggled at the Macron Stadium.
The financial situation the club is in has not helped and the Celtic manager would like a chance to manage the side during a more settled financial landscape.
Brown, who is fighting for the League One play-off places with Southend at the moment, spent six years with Bolton as a player and worked as assistant under Allardyce at the club for six years - so he would undoubtedly love to return to the club one day.
But for now Lennon remains and Brown is keeping his lips sealed on any discussions over his future.