"We'd like to thank Jose on behalf of everyone at AS Roma for his dedication and efforts since joining the club," said Dan and Ryan Friedkin.
Former Bayern Munich manager Carlo Ancelotti is set to take over as Napoli coach, according to reports in Italy on Tuesday.
Ancelotti, who was sacked by the Bundesliga champions last September, was reported to be holding talks with Napoli president Aurelio De Laurentiis in Rome on Tuesday night.
The 58-year-old Ancelotti and Italian film producer De Laurentiis are finalising details of a three-year contract.
Corriere dello Sport reported that everything was now in place for Ancelotti to take over the southern side, but only if Maurizio Sarri decides to leave the club.
Contact between De Laurentiis and the former AC Milan and Real Madrid coach has been ongoing for weeks amid the indecision of Sarri, who has a contract with Napoli until 2020.
Sarri indicated last Sunday that he was ready to leave the Serie A side he joined in 2015 after finishing runners-up for the second time in three seasons behind Juventus.
Ancelotti, who also had spells in charge of Chelsea, Juventus and Paris Saint-Germain, has three Champions League titles to his name as a coach. He has also won the league in Italy, France, Germany and England.
He was reported to have recently turned down the opportunity to coach the Italian national side to stay in club football.
Sarri, meanwhile, has been linked with English side Chelsea.
The 59-year-old former banker was also reported to have been contacted by Zenit Saint Petersburg, with the Russian club able to pay his eight-million-euro (USD 9.4 million) release clause.