Cooper, who replaced John Hughes as Pools boss at the end of last month, will be taking charge of only his second game against Forest at the City Ground, where he spent five years as a player in the 1990s.
Bradford made history by becoming the first club from the bottom tier to play in a major cup final at Wembley in February and Cooper feels their heroics will spur on all lower league clubs.
"It's a fantastic second game in charge for us, that's for sure," Cooper told the club's official website.
"They've just been showing the footage of Bradford's cup run last season on Sky Sports and I think a lot of teams below the Championship will be looking at what they achieved and be inspired by it.
"We will need to be organised, hard-working and brave in both boxes and if we are all of those things then anything can happen - it will be a big test, but one we will stand up to.
"It will certainly be a fixture I will be looking forward to a lot and it will give me immense pride to be able to lead my Hartlepool side out against Forest where I had five memorable years."