The 52-year-old is currently out of work having left Serie A giants Inter after guiding them to their first championship in 11 years.
Italian transfer expert Fabrizio Romano reports Conte does not want to take over at a club mid-season, and instead is keen to take on an exciting opportunity next campaign.
Clamour around a new manager at Barca is reaching fever pitch after boss Ronald Koeman's terrible start to the season, while Arsenal fans continue to show dismay at Mikel Arteta's tenure, which is yet to ignite.
But neither club reportedly appeals to Conte, who won the Premier League title with Chelsea in 2017 in his first season at the club.
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