Manchester United have been strongly linked with the Poland international this summer, but City joined the race earlier last month.
They were informed at that stage that Lewandowski's preferred destination was Bayern Munich. But Dortmund are unwilling to sell the 24-year-old forward to their Bundesliga rivals.
And the sale of Tevez to Juventus has re-opened the possibility of Manchester City going back in for the Dortmund striker.
With Tevez and Mario Balotelli gone, and Edin Dzeko heavily tipped to leave the Etihad Stadium, the Premier League title hopefuls may just have Sergio Aguero as a first-choice option next term.
The Champions League runners-up want £25m for a player who has one year left on his contract. Bayern Munich hope Lewandowski will run down his deal and join them on a free next summer.
The report claims City have dropped interest in Edinson Cavani over concerns regarding his wage demands and transfer fee, while a move for Liverpool star Luis Suarez would be difficult to pull off. Real Madrid would be his most likely destination were he to leave Anfield.
And Manchester United may not offer much competition for the signature of a player who was at one time their top summer transfer target.
David Moyes has cooled interest in Lewandowski in recent weeks, with the focus now thought to be on a new central midfielder.