The Irishman has been on trial with Town during pre-season and again impressed Boothroyd in Saturday's friendly defeat at the hands of Peterborough United.
The Town boss also ran the rule over Kevin Amankwaah and Liam Dickinson in that game but it is Deegan who is closest to being offered a deal.
“I’d like to offer Gary something and we are hoping to sort that out as soon as possible," Boothroyd told the official NTFC website.
Deegan was signed by Coventry City from Bohemians in 2010 and initially made a positive impression on supporters with his combative style, also chipping in with the occasional goal.
He was sidelined by injury throughout Boothroyd's brief reign with the Sky Blues and later moved on to Hibernian in the SPL.