After a summer transfer window where the club failed to bring in a string of transfer targets, Conte is keen for the reigning Premier League champions to make up for those missed opportunities and make significant additions to his squad during the January window.
The former Juve manager has been frequently linked with a move for his former defender Chiellini, whose current contract with the Serie A champions is set to expire at the end of the season.
Reports of a move for the 33-year-old centre-half have resurfaced with major doubts emerging over Luiz's future at the club, having been dropped from the Blues first-team by Conte.
Chiellini has played down talk of a move to Stamford Bridge himself after suggesting he will sit down to discuss a new deal with Juventus, with Conte now suggesting the veteran is very unlikely to leave Turin.
"Giorgio is a good player but he will want to finish his career at Juventus," Conte told a press conference ahead of Chelsea's Premier League clash with Arsenal on Wednesday. "It is right to finish his career in this way."
Conte has not ruled out bringing in another defender during the mid-season window however, adding Luiz will only be able to leave the club should the club find a replacement.
"Our squad is not big, for this reason it is impossible to send a player out if we don't get another player in."
With 34 players out on loan, Chelsea could be tempted to recall some of their brightest stars to bolster the first-team squad, as they did last January with Nathan Ake. Ruben Loftus-Cheek, excelling on loan at Crystal Palace this season, is among the clutch of players linked with an early return to Stamford Bridge, but Conte suggests the club will not be exploring the possibility of recalling players who are getting game time away from home.
"I don't think could be realistic," Conte said. "The players we send on loan are playing. I don't see a possibility for players to come back on loan."