Per Nick Ames of the Guardian, Conte said: "Everything is possible. If there is a possibility to find a good solution to improve the squad I think the club knows very well my opinion".
The Chelsea boss has vowed "I won't forget" Mourinho's criticism, after the Manchester United manager hit out at Conte over match-fixing.
The 24-year-old started only two Premier League games this term, has been restricted to substitute appearances as Antonio Conte preferred to play Eden Hazard as a forward ahead of his fellow Belgian in the absence of Alvaro Morata.
"He's a great player and knows very well that in my first season at Juventus we tried to buy him from Udinese, but then he made a decision to go to Barcelona", he said.
But Capello believes both men have lost control and that fellow Italian Conte may have underestimated how well Portuguese Mourinho handles the press.More news: Cavusoglu names main causes of discord between Turkey and US
Mourinho, former manager of Inter Milan and Chelsea, had struck a nerve. Last year, we missed the icing on the cake.
Chelsea star Thibaut Courtois is demanding one thing from his Stamford Bridge teammates over the next few weeks as Antonio Conte sets the bar.
When asked if he was content at Chelsea given all the speculation about his future, he added: "Yes, I'm happy". In football now it is very hard to predict if you can stay many years with one club, especially in England.
Conte said: "I said "hello".
Chelsea are looking at options to loan Charly Musonda but have been reluctant to loan Kenedy, who has not had much game time but is operating as a back-up to Marcos Alonso at left wing-back. I have a lot of experience to deal with this situation.
As for Conte, should he leave London this summer as is widely reported, he will undoubtedly be linked with a return to the national side as they still seek a replacement for Giampiero Ventura.