Chelsea’s goalless draw at Norwich, on Saturday, means the Blues face an FA Cup third-round replay at Stamford Bridge on January 16.
The visit of Norwich will come between legs of the League Cup semi-final with Arsenal, the first of which takes place on Wednesday. The second is on January 24.
And should Chelsea beat Arsenal in the two-legged semi-final, their scheduled, February 25 Premier League clash at Old Trafford will have to be moved, as the Carabao Cup final, at Wembley, takes place on that date.
Conte made nine changes at Carrow Road and is expected to revert to his first-choice line-up to face the Gunners, with whom Chelsea drew 2-2, in the Premier League, last week.
Conte told Chelsea TV: “When you play every three days, and you have to play many games, it means you are facing every competition.
“Now, on Wednesday, we have to play a semi-final against Arsenal. I think we deserved to reach this target.
“It’s very important, in this moment of the season, to have all the squad in the best physical form, because you have to play a lot of games and everyone must be ready.”
Conte’s and Mourinho’s feud intensified on Saturday. The Chelsea head coach called the United boss a “little man” and “fake”, before issuing an apparent challenge: “Me and him, face-to-face. I’m ready. I don’t know if he’s ready.”
Simmering tensions, between Conte and his predecessor as Chelsea boss, ignited on Friday, when Mourinho made reference to match-fixing allegations.
Conte had been accused of failing to report his knowledge of an incident of attempted match-fixing, during his time as Siena boss, in 2011, and he duly served a four-month touchline ban, in 2012.
He was acquitted of any wrongdoing, over the matter, in 2016, shortly before taking over at Chelsea and Mourinho’s revisiting of the matter irked the Blues boss.
“I consider him a little man, I consider him a man with a very low profile,” Conte added.
“When there are these types of comments, before (making them) you have to know very well the truth.”
Conte also criticised Mourinho for, in February, 2017, attending a media conference wearing a training top with the initials ‘CR’, following Claudio Ranieri’s sacking by Leicester.
Conte added: “He offended Ranieri for his English. Then, when Ranieri was sacked, he put on a shirt (with initials on) for Ranieri. You are a fake.
“If you want to fight a person, you try to kill this person. And then, after two years, you try to help this person, because maybe it’s good for you, for your profile.”
Conte hopes new signing, Ross Barkley, will play his way into England’s World Cup squad.
Barkley signed for Chelsea from Everton, on Friday, for a cut-price fee in the region of £15m (€16.9m) as his Toffees contract was due to expire this summer. He hasn’t played since May, due to a hamstring injury, which required surgery.
The Blues boss is reluctant to put a timescale on when Barkley will be available, but hopes for a swift impact.
“We have five months to show he deserves a call with the national team for the World Cup,” Conte said. “I hope (he gets one), because it means he will do very well with us.”