Ultimately though, it sounds as if he's waiting for the backing of the club in the transfer market, and if that doesn't arrive sooner rather than later, then Chelsea could be looking for a new coach.
The report claims Conte also seeks a direct line of communication with owner Roman Abramovich, cutting out any and all middlemen within the club's executive structure.
Despite leading the club to a dominant Premier League title win, there have been rumours for several months that Conte may consider his position at the end of the season.
Costa, 28, who is under contract with Chelsea for another two years, said last week that Antonio Conte does not count on his services for the 2017-18 campaign.
The nerazzurri had offered him € 15 million a year, but the former Juve boss opted to stay for one more year at Chelsea.
The London inferno - could it happen here?
More than 1 million pounds have been raised to help those affected by the massive blaze which ripped through the building. There is no way that rich people would be living in a building without adequate fire safety.
The Spain global, 28, smashed in 20 goals to help the Blues secure their second Premier League title in three years last season.
Standard Sport revealed in March that Chelsea had promised Conte he would be given significant funds to strengthen the squad during the transfer window.
Conte has told Costa via text message he can leave this summer, but the Chelsea hierarchy are keen to keep hold of the striker.
There is a creeping sense of unease among Chelsea supporters that the board aren't doing enough to back Conte - deja vu perhaps from the summer of 2015 when Jose Mourinho asked but didn't get.
According to French newspaper L'Equipe, Chelsea have offered £26m, but Monaco want up to around £44m.
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