Kane has been pushing to leave Spurs and join City, their opening Premier League opponents, according to widespread reports.
The England captain returned late in pre-season following Euro 2020 and has had to quarantine, meaning his involvement in training was delayed.
Nuno had planned talks with Kane, which have now taken place, but the Tottenham boss was revealing little on Friday.
"Harry joined the group today," Nuno told a pre-match news conference. "He trained, we talked. Of course, it's a private conversation.
"Everything is okay. He's preparing himself, like Bryan [Gil], like [Cristian] Romero, players who joined us later. We have to be careful but everything's okay."
On his availability for Sunday, he added: "We still have the session tomorrow [Saturday] to decide.
"Romero, Bryan, Harry, players that do not have too many sessions with us, we have to think. We still have the day tomorrow to make decisions."
Nuno was then asked outright if he expected Kane to remain a Tottenham player beyond the end of the transfer window.
"He's here with us. He's a Tottenham player. He's here with us," he replied.
"We have to think about tomorrow, prepare the training session of tomorrow, and go day by day. All the players that have worked with us are our players."
Tanguy Ndombele is another player at Nuno's disposal, but he has merely been on the fringes of the squad in pre-season.
"There's always a reason in all the decisions we make. There's always a why," the coach explained when asked if Ndombele had a Spurs future. "We think, we talk and then we decide.
"We believe that Tanguy did not perform in the pre-season matches because we considered that he's not at the right moment for him to be with the group in terms of competition."
Tottenham have also been linked with incoming transfers, including Inter's Lautaro Martinez, and Nuno acknowledged they were working on incomings.
"The squad needs balance. We have a very talented squad, but it needs to be balanced," he said. "Everybody knows we are working very hard, but it's always hard to improve something that is good.
"We have to be really, really accurate on the players that we bring, because they have to bring things that we believe can make us better and strong. That is not easy, because we have quality players with us."