Last month, Bournemouth made the surprise decision to part ways with the Englishman, just over three months after their return to the Premier League.
The Cherries board made the decision on the back of Parker seemingly not wanting to keep in line with their strategy in the transfer market.
Parker had previously been critical of the lack of significant incomings at the Vitality Stadium, suggesting that the club required more established names to compete in the top flight.
Despite the circumstances behind his departure, the 41-year-old left with 28 wins and just 13 defeats from his 55 matches in charge, three of the losses coming against Manchester City, Arsenal and Liverpool earlier this campaign.
Having also earned promotion with Fulham in his first managerial job, Parker is likely to be in the running for any domestic roles which become available in due course.
Nevertheless, according to FootMercato, Nice may be ready to explore the possibility of appointing Parker as their new head coach.
Lucien Favre was only given that position as recently as June, but the 64-year-old has failed to make the expected impact in the South of France.
Just three of his 12 matches in charge in all competitions have ended in victory with just eight points being collected from as many matches in Ligue 1.
With draws against FC Koln and Partizan Belgrade being recorded in the Europa Conference League group stages, the powers-that-be at Allianz Riveira are said to be contemplating a change in direction.
Nice were allegedly hoping to bring in former Paris Saint-Germain boss Mauricio Pochettino, but it is said that the Argentine is unlikely to make the switch to the Eaglets.
Instead, it is reported that club advisor Iain Moody has pointed the French outfit in the direction of Parker, who may be willing to take on the challenge after a month out of work.
Nice's first-team squad contains a wide array of former Premier League players, including Kasper Schmeichel, Mads Bech Sorensen, Ross Barkley, Joe Bryan, Aaron Ramsey and Nicolas Pepe who were all signed during the most recent transfer window.
A trip to Parc des Princes to face Paris Saint-Germain awaits Nice when Ligue 1 resumes after the international break.