Maurizio Sarri was unable to give guarantees over the futures of Eden Hazard and Thibaut Courtois amid speculation the Belgian pair could leave Chelsea this summer.
New Blues head coach Sarri faces a battle to keep hold of his star players after replacing Antonio Conte at Stamford Bridge.
Forward Hazard and goalkeeper Courtois, who are both recovering after helping their country finish third at the World Cup, have been heavily linked with Real Madrid.
Courtois's contract expires next summer, while Hazard has an additional 12 months on his deal.
Speaking at his unveiling as Chelsea manager, Italian Sarri told a media conference of his disinterest in the transfer market.
"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," said the 59-year-old.
"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 would not respond to further transfer questions, but expressed some doubt over the central midfielders at his disposal.
"I cannot name any names because I don't know who these people are," he added.
"I spoke to the football club and I said a pinch of quality is lacking in centre midfield for a certain kind of play. Otherwise they're at a very high level."
Asked specifically about club captain and Chelsea's longest-serving first-team player Gary Cahill, who was on Tuesday linked with a move, Sarri said: "With respect to Cahill, I think he can still give us a lot."
Sarri's anticipated appointment was confirmed last Saturday, 24 hours after predecessor Conte was sacked.
He paid tribute to his compatriot, 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. He is an extraordinary manager," he added.
"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."
Conte was dismissed despite following a Premier League title success in his first season in England with winning the FA Cup in May.
Former Napoli boss Sarri, who has never won silverware, insisted the only target set by Chelsea was to be competitive this season.
He also refused to be drawn on any conversations with owner Roman Abramovich. Russian billionaire Abramovich has been in dispute with UK authorities over the lack of a visa renewal.
"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.
"Honestly I hope I will be able to fill in this gap with the club, the difference between doing well and winning.
"They (Chelsea) have just asked me to build a season to be competitive in all competitions. Then during the season we'll see whether or not we want to have more specific objectives."
He added: "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."