Kane's future at Spurs remains in doubt after he made clear his desire to leave the club. Manchester City reportedly had an offer of £100million rejected earlier in the transfer window, though the reigning champions still remain the most likely landing spot for last season's Golden Boot winner.
After playing a key role in England’s run to the Euro 2020 final, the 28-year-old did not report for pre-season training on Monday, as the club expected.
Kane released a statement on social media explaining how he would return for duty on Saturday, making clear that was always the plan while adding: "I wouldn't do anything to jeopardize the relationship I have with the fans who have given me such unwavering support during my time with the club."
While he completes a period of isolation and goes through physical testing, Spurs continued their preparations on Sunday with a 1-0 win over Arsenal.
"Harry is with us," Nuno, who was appointed as Tottenham's new head coach at the end of June, confirmed after the game.
"He has to quarantine at The Lodge, but he has already done his first day with the sports scientists, so he is with us.
"I will speak with Harry as soon as possible."
Whether viewed as a potential replacement or a new strike partner for Kane, Tottenham have been linked with a move for Inter forward Lautaro Martinez.
The Serie A side have already sold Achraf Hakimi to Paris Saint-Germain as they look to ease their financial situation in the offseason, while Romelu Lukaku is expected to complete a return to Chelsea in the coming days.
Martinez could be set to follow Inter colleague Lukaku to London, though Nuno was unwilling to discuss potential new arrivals.
Asked about the Argentina international, he replied: "I will not speak about any player. I will only speak about my players, Tottenham players, nothing else."
Son Heung-min scored the only goal against Arsenal, firing past Bernd Leno in the 79th minute after being picked out by Japhet Tanganga's square pass.
Spurs start the new league campaign next Sunday, hosting Manchester City.