The Irishman joined Town last summer, and on the sale of Charlie Goode to Brentford, was made first team skipper by then manager Keith Curle
The contract Bolger signed on his arrival at the PTS Academy Stadium was for 12 months, with an option for the player to trigger an extra year if he wanted to.
The former Fleetwood Town, Lincoln City and Southend United man must now make up his mind if he wants to stay or not, and Brady doesn’t want things dragging on.
Under Curle, Bolger was a regular at the heart of the Town defence, making 30 starts in all competitions.
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Bolger also started in Brady’s first game in caretaker charge in February, the 2-0 home loss to Burton Albion, but then didn’t feature again.
Brady instead opted on a centre-back pairing of Lloyd Jones and Fraser Horsfall. with Bolger relegated to the bench, where he remained for the rest of the season without getting a single minute of action.
Asked if he had spoken to the 29-year-old about his situation, Brady said: “We have sat down together and we have had some really good conversations.
“Cian has that option in his contract in his favour, and he will have a couple of weeks to tell us his decision.
“That is where we are at with him at the moment.”
Tuesday was Brady’s first retained list as a senior manager, although he has in the past had to deal with youth players coming to end of their contracts so it wasn’t a process completely alien to him.
That said, the Town boss, who was only handed the job on a permanent basis on Saturday, admitted it wasn’t the best of days.
“It’s a job that has to be done but it’s never nice,” said Brady.
“Some of the players we’ve let go have been unfortunate with injuries or some haven’t had the opportunities they would perhaps have liked but we have to re-build and be stronger next season.
“Yes we were relegated, but what I can’t fault is the attitude of the players which has been excellent.
“It’s tough for a footballer being out of contract and especially during these times.
“We have got to be sympathetic of that and if they want my help I will do all I can to help them find a new club.
“Every player moving on parts on good terms and we wish them well.”