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The Serie A champions have endured an inconsistent start to the new campaign under Garcia, with five wins, three defeats and two draws from their first 10 games in all competitions.
Conte, meanwhile, has been out of work since he was sacked by Tottenham in March.
According to widespread reports in Italy, Conte is now due to meet with Napoli president Aurelio De Laurentiis to discuss the possibility of returning to Serie A and replacing Garcia, who was brought in as Luciano Spalletti’s successor in the summer.
It’s understood that Conte would accept a move to Napoli, but would demand a significant say in the club’s transfer strategy before agreeing a deal.
When asked about a possible move to Napoli on Tuesday evening, Conte said: ‘For now I’m enjoying my family, I made a clear choice when I left England.
‘Then you know that a lot of things can happen along the way.’
Meanwhile, former Napoli centre-back Kalidou Koulibaly has urged the Italian club to give Garcia more time.
‘Garcia is a great coach and he needs time to adapt, just like other coaches did in the past,’ Koulibaly said in an Instagram live interview.
‘The players are with him, I spoke to two or three of them and they confirmed that to me.
‘They just need to keep working and everything will go well. I hope for him that the club has patience to let him get on with the job.’
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