ESPN reported on Monday that City were readying a £100 million offer for Kane that could include players heading to Spurs as part of the agreement.
Reports have suggested Sterling is one of the names in the frame, along with Gabriel Jesus and Aymeric Laporte, but sources have told ESPN the England winger is not open to the idea of being considered in the deal.
Sources close to City and Tottenham told ESPN a formal offer for Kane has not been made.
Sterling has been a key part of City's success under Pep Guardiola, winning the Premier League title three times.
However, the 26-year-old lost his place in the starting XI towards the end of last season as Guardiola favoured Phil Foden and Riyad Mahrez. All three started the Champions League final defeat to Chelsea.
He has two years left on his contract after signing an extension in November 2018.
Sources have told ESPN that if he were to leave City this summer, it would be on his terms rather than as part of another deal.
Sources have told ESPN that even if City made a £100m bid, it is likely to be rejected by Spurs chairman Daniel Levy, who values the striker at more than £150m.
Kane still has three years left on his contract after signing a long-term deal in 2016.
The 27-year-old's future has also been complicated by Spurs' ongoing search for a new manager after the dismissal of Jose Mourinho last season.