Chelsea are confident they will make three to four more transfers before the window closes at the end of next month, but Southampton defender Virgil van Dijk won't be one of them.
Conte spoke at the weekend about the need for 'many more' signings if Chelsea are to compete on all fronts in the forthcoming season.
So far they have signed four players this summer - Willy Caballero, Antonio Rudiger, Tiemoue Bakayoko and Alvaro Morata.
But Chelsea have allowed many more players to leave permanently or on loan to leave the squad lacking strength in depth.
Conte reiterated that point a few days ago, admitting Chelsea are in danger of lacking the tools to compete with the likes of Manchester City, who have now spent £230m on new personnel during the close season.
The board are working overtime to acquire the targets that Conte has asked for but long-term target Van Dijk will not be moving to Stamford Bridge.
The Dutch international was Chelsea's first choice to strengthen the backline, but they have been scared off by Southampton's determination not to sell.
It is believed Liverpool are going to give up the chase too, despite the former Celtic star making it clear he wants a move to Anfield.
He has been ordered by Southampton coach Maurico Pellegrino to train on his own because he is not in the 'right frame of mind' to be with the rest of the squad.
Chelsea are exploring other areas of the pitch to improve upon, as they believe the arrival of Rudiger, plus the return from loan of Andreas Christensen, has boosted their centre half options enough.
In Pictures | Arsenal vs Chelsea | 22/07/2017
Standard Sport has consistently stated that another wing back, central midfielder and forward are Conte's main priorities.
They are no closer to buying Sandro from Juventus, but they are struggling to find alternatives at full back after Manchester City beat them to both Danilo and Benjamin Mendy.
There is an acceptance within the club that acquiring targets has become a lot more difficult, particularly in England, because of the amount of TV prize money in the game, meaning clubs are no longer under pressure to sell.
Despite this, Chelsea remain desperate to give Conte what he wants to make sure Chelsea enjoy another successful campaign with the Italian in charge.
Chelsea will be playing in the Champions League for the first time under Conte next term, on top of the three domestic competitions.