Maurizio Sarri said he wants to keep Eden Hazard and Thibaut Courtois at Chelsea, but was unable to offer assurances over the Belgian pair's future.
Former Napoli coach Sarri was confirmed as the new Chelsea manager on Saturday. One the same day following Belgium's win over England in the World Cup third-place play-off, Hazard said "it might be time to discover something different" after six years at Chelsea. On Sunday, goalkeeper Courtois followed suit by suggesting he could also leave Stamford Bridge.
Speaking at his unveiling as Chelsea manager at Stamford Bridge on Wednesday, Sarri told a media conference of his disinterest in the transfer market.
After an opening address in English, Sarri spoke in his native Italian, saying: "Clearly we would always like to keep all the strongest players. This is what any manager wants to do, this is what any club wants to do.
"Then we will have to see how the transfer market will go over the next few days. I think that I am one of the few managers who is bored by the transfer market. I don't want to talk about the transfer market and I'm not that interested in it."
Sarri said he "did not want to say anything wrong" in his first media conference in explaining his preference to speak in Italian.
"Well, for me this is a difficult challenge, but a fascinating one," he said. "I know it will be very difficult and here we have the strongest coaches in the world and the strongest players in the world.
"I know this will be an extremely difficult challenge for me. I have not asked anything of anyone. I want to have this experience also based on my mistakes."
He also paid tribute to his compatriot Antonio Conte, who was sacked last week, while also saying he will need time to impose his methods, particularly with many players still absent after the World Cup.
"Antonio has reached incredible results here and elsewhere," Sarri said. "He is an extraordinary manager. Clearly I play in a slightly different way so it will take some time for the squad.
"This is a post-World Cup time. It will take some time to build a slightly different way of playing. All good things Antonio Conte did must be left. They must not be changed."
Sarri would not respond to further transfer questions, but cast doubt on the futures of his defenders.
"I cannot name any names because I don't know who these people are," Sarri added.
"I spoke to the football club and I said a pinch of quality is lacking in centre halves for a certain kind of play. Otherwise they're at a very high level. At the end of the transfer window it will be up to me."
Sarri insisted the only target set by Chelsea was to be competitive this season, while he refused to be drawn on any conversations with owner Roman Abramovich.
"They have just asked me to build a season to be competitive in all competitions," he said. "Then during the season we'll see whether or not we want to have more specific objectives.
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"Our owner is an extremely reserved person, so I don't want to start a work relationship with him by speaking about private things.
"I think this is an extremely private relationship and I would also hope this relationship is respected."
Sarri is yet to win a trophy as a manager, but earned plaudits for his performance as Napoli manager, and hopes to end his silverware search with Chelsea.
"It's true I haven't won anything, but I have been in Serie A for four or five years and apart from Juventus, no one has won anything," he said.
"I think we have worked very well and the difference between working well and winning often is minimal.
"Honestly I hope I will be able to fill in this gap with the club, the difference between doing well and winning."