Barkley has signed a five-and-a-half-year deal at Stamford Bridge, finally moving to Chelsea after a summer transfer collapsed on deadline day due to a hamstring injury.
Chelsea have given Barkley the No.8 shirt that was once worn by the club's all time top goalscorer Frank Lampard, and Conte seemed pleased with the attributes his new signing will bring.
"We are talking about a player with great potential," Conte said at Cobham Training Centre. "He is a complete player but at the same time he is very young and he has just started his career.
"He has this great opportunity to play in a great club, with ambition and great targets, and also to put yourself in this new challenge. [He's a] complete because he has it all. He has stamina, strong physically, good technique and he is a complete player.
"He is a modern footballer. I have to still see him and then we have the opportunity to work together and understand how much time he needs [until he makes his debut]."
"The most important thing is these players must be good [not just English]. Then, for sure, when I was in Italy we had a great base of Italian players. I think that this could be positive because English players understand this league because they grow up in this league.
"For Chelsea also it would be positive to buy English players because we lost important players like John Terry, Frank Lampard from this club, this country. This could be positive."
Conte earlier responded to criticism from Jose Mourinho that fellow coaches act "crazy," with the comments seemingly directed at the likes of the Chelsea head coach. He also commented on Arsene Wenger's complaints about Eden Hazard's alleged dive to win a penalty on Wednesday as Chelsea drew 2-2 with Arsenal at the Emirates Stadium.
Conte said he's not looking to create the "cinema" that other managers seem interested in amid the renewed war of words between coaches in the Premier League.
"I must be honest, I don't read [comments from other managers]," he added. "The only opportunity to know about these situations is during the press conference. I am not prepared like other people to make cinema because there are other people who prepare to have a cinema in the press conference.
"Before the game and during the game, I am not this type of person. At the same time, when I start to listen with regularity to this situation it is right to answer because it is funny and I laugh a lot.
"Now it is very difficult to do only cinema. Maybe in the past with the cinema it was enough. Now you have to show football knowledge and the cinema is not enough for the coach. In my one year and a half I never talk about other coaches — if I did, only to make compliments, if I saw a well organised team.
"Normally when I speak about other coach it is only to make compliments — otherwise I stay silent. But in this situation you must have respect.
"I think I do have this, but at the same time I am starting to be a bit annoyed because once, twice [I am attacked], and then the people who know me well in Italy [know how I react]. For this reason you must. If you want to go to fight with me, I am ready.
"I am improving a bit my English because this is the real problem for me — otherwise we can go to fight. I am ready to fight for me, my players the club, with everyone. I have no problem."