Antonio Conte has masterminded Chelsea's rise to the top of the Premier League this season.
The former Italy head coach looks set to win the title in his first year in England, while Chelsea are also into the FA Cup semi-finals.
But Italian newspaper Tuttosport claim Conte could quit west London for a return to his homeland at the end of the season.
Chelsea owner Abramovich (centre) wants to sign Neymar to keep Conte at the Blues
Antonio Conte's secret scouting mission to Italy
Mon, February 6, 2017
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Inter want Conte
According to the report, Chelsea's billionaire owner Abramovich is worried Conte will ditch the Blues and head to Inter Milan.
Conte is said to have been wooed by Inter's new Chinese owners, with the San Siro club now believing they can challenge Juventus for the Serie A title and Champions League honours.
Inter are supposedly flush with cash following Suning Group's takeover last year.
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The new owners have already sacked one manager and appear willing to axe Stefano Pioli at the end of the current campaign in order to facilitate Conte's arrival.
Last week The Sun claimed Inter were willing to pay Conte £13million a season a catapult them to the top of European football.
Conte is supposedly considering his future at Chelsea
Suning Group took over Inter Milan last year
Inter Milan sit fifth in Serie A but believe they can challenge Juventus for the title next season
Abramovich is said to have offered Neymar to Conte as a sweetener for keeping the manager at Chelsea.
But Conte, 47, appears to be having none of it.
According to the claims, he has no interest in the Brazil international.
Barcelona would likely fend off any attempts to lure Neymar away from the Nou Camp, having slapped a £170million release clause into his most recent contract signed last October.
The 25-year-old's current deal lasts until 2021 and Barca are in no position to sell.
Roman Abramovich is desperate to keep Conte at Chelsea
Tuttosport claim Conte is not interested in Neymar
Neymar to Chelsea
However, no player is beyond the reach of Abramovich and Tuttosport claim the 50-year-old would fund a bid for any player Conte wants in order to keep the manager in place.
Last week Neymar suggested he would one day like to play in the Premier League.
“The Premier League is a championship that amazes me," he said.
Barcelona have Neymar locked down to a long-term contract
“I like the playing style and the teams. And who knows, someday, I would like to play at it, yes.
“I admire Manchester United, Chelsea, Arsenal, Liverpool — these are the teams that are always there fighting.
“And then you have high-level coaches like [Jose] Mourinho and [Pep] Guardiola. These are coaches with whom any player would like to work.”
Abramovich is keen to get deals sorted ahead of the next transfer window after Chelsea somewhat rushed through deals last year, with David Luiz arriving late on deadline day and Conte unable to source more than one new striker.