Madrid-based sports radio station Marca – affiliated to the newspaper – reported that the Spain international would move to Eastlands for the fee of 28 million euros (£24m).
If the move does transpire, Negredo would join former team-mate Jesus Navas at Eastlands after he joined for £15m.
He has long been linked with a move to the Premier League, with Tottenham Hotspur previously tipped as a destination.
Discounting the reported fee, City seems like an unusual destination given his reputation as a bustling poacher - Edin Dzeko would presumably leave the Premier League runners-up, and he is widely regarded as a superior target man.
Negredo has scored 70 goals in 139 Liga appearances for Sevilla and six in 14 for Spain.