The Irishman is out of contract following a stint at Bournemouth last season, and has also recently been linked with Sunderland and Middlesbrough.
The versatile 30-year old has struggled with injury issues in the past and was unable to earn consistent game time with the Cherries as they earned promotion from the Championship.
Brady played six league games, starting twice, as Scott Parker’s side earned 2nd in the table.
However, the Manchester United academy graduate has enjoyed Premier League experience with Hull City, Norwich City and Burnley.
He is currently training with the squad as pre-season gets underway for Ryan Lowe’s side.
This gives both parties a chance to get a feel for each other as they assess whether this is a viable move going forward.
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Brady joins fellow trialist Ben Woodburn, as Preston look to potentially bring both into the team ahead of the next campaign.
The 43-year old will be hoping to improve his first team squad as the club looks to climb the table compared to last season.
PNE came 13th in the table last term, finishing 11 points adrift of the play-off places.
Brady has had a difficult couple of years, but if he can regain his fitness ahead of the new campaign then this could be a very good signing.
He can play in attack or in defence on the left flank, which offers the team a lot of options.
Brady’s set piece delivery is also top notch, which could prove to be a valuable weapon to have in the team’s arsenal.
With him potentially arriving as a free agent, this transfer could be worth a chance due to the little risk involved if things don’t work out, but this could be Brady’s last chance to show he can compete at this level.