The 41-year-old has yet to take on a new role since leaving Chelsea, though there has been speculation over a possible return to France.
OGC Nice are reported to have made contact with Rosenior recently, but the Englishman is said to have turned down the opportunity to take over there.
According to Foot Mercato, another Ligue 1 club has now shown interest in bringing Rosenior back to French football.
The outlet reports that Paris FC have included the Englishman on their list of potential candidates for the head coach role ahead of next season.
Current Paris FC head coach Antoine Kombouare faces an uncertain future at the club, prompting the Ligue 1 side to explore possible replacements as they look to plan for the upcoming campaign.
Paris are also reported to have made an approach for Bruno Genesio, though he looks instead set to take charge of Olympique Marseille, narrowing the list of candidates still under consideration.
Paris FC finished 11th in Ligue 1 last season, a campaign that leaves room for the club to reassess their coaching set-up heading into the new campaign.
Rosenior previously held spells in his coaching career at Derby County and Hull City before moving into European football with Strasbourg, where he guided the club to a seventh-place finish and qualification for European competition.
His time at Strasbourg, where Chelsea's ownership group also holds influence, was seen as instrumental in eventually earning him the move to Stamford Bridge earlier this year.
That same ownership link initially fuelled belief that Rosenior could thrive at Chelsea, given his familiarity with the club's recruitment and footballing philosophy from his time in France.
Instead, his tenure in west London lasted only a matter of months before the club opted to make a change, leaving Rosenior to consider his next step outside the Premier League for now.
Whether Rosenior opts to return to Ligue 1 with Paris FC remains to be seen, with the Englishman still weighing his next move following his brief and difficult Chelsea spell, and Nice's approach already turned down in recent weeks.