Pep Guardiola and Nuno Espirito Santo both refused to be drawn on Harry Kane's future after Tottenham's 1-0 win over Manchester City.
Kane did not feature as Spurs opened their Premier League campaign with victory in front of a full home crowd.
Defending champions City lacked a cutting edge, emphasising why they are keen to sign the England captain.
"We are very lucky to have him," Nuno, in his first match in charge, told Sky Sports.
Asked whether Kane would feature in their next Premier League fixture against Wolves on Sunday, Nuno added: "Harry Kane is one of the best players in the world, honestly.
"He has to get ready and help the team. We still have to go to Portugal [on Thursday for the Europa Conference League] then we think about Wolves."
Kane was said to have been in the stadium after training on Sunday morning, having returned to the club on Friday.
"Harry worked this morning [Sunday]. He is preparing himself and when he is ready he will join the group and help the team," Nuno added.
Manchester City forward Raheem Sterling - an England team-mate of Kane - said Tottenham were able to do the "most important thing in football, which was put the ball in the back of the net when we couldn't".
It was their first league game since the departure of striker Sergio Aguero, who joined Barcelona this summer after 10 years at City.
But manager Guardiola insisted he was "delighted" with City's attacking options, declining to say whether the result would intensify his club's pursuit of Kane.
"We have the same guys as last season, just without Sergio [Aguero]," Guardiola told BBC Radio 5 Live.
"I'm so delighted with the same guys who scored a lot of goals. I'm more than delighted with this."
Guardiola went on to describe the debut of £100m record signing Jack Grealish as "excellent".
"He played with a personality and created chances. Unfortunately we could not win for him on his debut but he played really well," he added.
"He doesn't lose the ball. He is so dangerous close to the box."
'There is always something to improve'
Tottenham 1-0 Manchester City: Nuno Espirito Santo 'very proud' of Spurs after opening winIt was Nuno's first game in charge of Spurs and he said he was "very proud" of the performance of his players against the defending champions.
"Amazing! It was a good day. Hard work for the boys. The distance they covered, the balance, the fight..." he said.
"There is still a long way to go but most of the things, the boys did well. We are [getting to know] each other better and it is about creating this energy between us to keep us moving forward.
"There is always something new and always something to improve."
'It is normal with not much preparation'
Manchester City manager Pep Guardiola says new signing Jack Grealish was 'excellent'Manchester City were without England midfielder Phil Foden through injury while Kevin de Bruyne came on as a substitute having not done "one full training session" since returning from international duty with Belgium at Euro 2020.
"It is normal for a season with not much preparation. The spirit was good but we lost," said Guardiola.
"I am more than surprised how good we have done many things. A lot of players arrived too late from the Euros, from Covid, for many things.
"Players come back and every week will be better. [Kevin de Bruyne] has not done one full training session, he needs to train. He will need time to play 90 minutes."
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