Inter handed Icardi the number seven shirt for the 2019-20 campaign in a move that indicated he is expected to remain at the club, where he was stripped of the captaincy last term.
The 26-year-old was widely expected to leave in the close season and was linked with Juventus and Monaco.
However, with Icardi still at Inter and the arrival of Romelu Lukaku from Manchester United, it appears Conte will be left with a player deemed surplus to requirements.
Asked about the effect of Icardi's continued presence by the media, Conte said: "I have great respect for everyone, but I don't feel any disturbance.
"We are working hard, we know full well what approach has been taken with the player, but it is not causing any disturbance for me."
Inter open against Lecce at San Siro on Monday, with Conte making clear that the aim for his side is to close the gap on last season's top two, Juventus and Napoli.
The Nerazzurri finished fourth, 10 points behind second-placed Napoli, but Conte believes Lukaku's arrival can boost their chances of improving this term.
"Lukaku arrived full of enthusiasm," said Conte. "He is a very joyful guy to be around and the team immediately welcomed him into their hearts.
"He was on the margins of the Manchester United squad for a while, so is not at 100 per cent, but has immense potential and can improve in every area.
"I tried him out alongside Lautaro Martinez, Matteo Politano and Sebastiano Esposito, so I am pleased with the synergy that is forming between these players.
"I always said that I wanted to feel even a one per cent chance of competing for victory. We are building something important here and I can say that the chase is on.
"We aim to close the gap, which is pretty large, from the top two. I don't set limits, only time will tell what we are fighting for, but we've got to work even better than the rest if we want to achieve something extraordinary."