Naden, who only joined the Bulldogs from Penrith at the end of last year, was immediately included by the Tigers for Friday's clash with Canterbury at Leichhardt Oval.
The intriguing match-up may have an extra element with former Tigers coach Potter looking set to take over in a caretaker role with the Bulldogs for the remainder of the season.
A two-time premiership-winning player with the Bulldogs, Potter coached the Tigers in 2013 and 2014 but failed to reach the finals in either campaign.
The 58-year-old is currently coaching Bulldogs' feeder club Mounties in the NSW Cup.
Another candidate for the interim role was David Furner, but he has been listed in his current position as an assistant for Friday's game on the Bulldogs' team sheet, suggesting he won't be taking over.
The Bulldogs sit last on the ladder with just two wins from their first 10 matches this season.
Canterbury's poor start to the campaign led to Barrett quitting as the club's head coach on Monday having won just five of 34 matches in charge.
Naden, part of Penrith's 2020 grand-final team, quickly followed him out of Belmore having scored one try in eight appearances for the Bulldogs.
The 26-year-old's exit doesn't appear to be the only one after Barrett's departure with former player and assistant coach Steve Turner not named among the off-field staff in Tuesday's team list.
High performance manager Dan Ferris, who worked with Barrett at Manly, is also reported to have been let go by the Bulldogs.
Star recruit Matt Burton is another who is expected to depart Canterbury.
The 22-year-old has an option in his favour for the final year of his two-season deal and would be free to talk to other clubs if he decides to quit the Bulldogs at season's end.
Fellow newcomers Matt Dufty and Paul Vaughan have been linked with moves to English Super League with neither having a deal on the table from the Bulldogs beyond this season.
