Conte is keen for Lloris to extend his stay at the Tottenham Hotspur Stadium and says talks are under way between the parties.
He said: “I think so, I think that they have started to talk.
“You know very well what I think about Hugo. Also previously I spoke and said that he’s our captain, he is a top goalkeeper for us, he has great experience.
“He knows very well Tottenham. He loves this shirt and this badge. For me he is an important player and I’m sure that they are going to find a solution for him to continue to play with Tottenham.
“I think and I repeat because I am not the person that speaks to renew the contract with the players. There is the club and the people that do this. But for sure I am very confident about this situation to be positive.”
Whether there is any other business during the January transfer window remains to be seen as Conte waits to see how the club will respond to his recommendations given in a meeting earlier this week.
Spurs are thought to be keen on strengthening a number of key areas, including at right wing-back, before the end of the month, but this is not a period in which the club have traditionally been active.
Conte says he would like any business done as soon as possible, but accepts it is not that simple.
“The transfer situation is not easy and a lot of time you have to wait for players at the end of this period to make new contracts,” he said.
“I have the experience to know this and understand this and for sure every coach would like to have the players very soon.
“But the club has to take the best decision on this aspect and the important thing is the club knows my vision about the present and then the future and they have to decide the way they have to go.”
Conte enjoyed the chance to speak to chairman Daniel Levy and managing director of football Fabio Paratici about his evaluations of the current squad based on his first two months in charge.
The Italian was forthright and open in his findings.
“It was a good meeting also because when you have the possibility to speak to the owner and the sporting director — with Paratici I have the possibility to speak every day — but to have the possibility to speak with our owner it was important,” he said.
“Also because I like to have this type of relationship, to be honest and to always tell the truth. You know I don’t like to tell a good lie to keep a good relationship or to show me very soft or to be too polite. It was good to tell the truth and it was a good meeting.
“Now for me it’s OK, I asked the club time to take my evaluation.
“The club asked after one month to have a meeting and I said no, I prefer to have another month to make the right evaluation.
“It’s honest, to give more time to me and also the players, to show me who deserves to stay here.
“Now the situation is very clear and I had this meeting, I was satisfied to have this conversation with the owner and now it’s OK for me.”