The Serie A giants had originally made Chelsea’s Fernando Torres their number one target, but have turned their attention to his international teammate.
Negredo, who only moved to England last summer, scored twenty-three goals in all competitions for City during the 2013/14 campaign on route to winning both the League Cup and the Premier League title.
However, he failed to score in the final four months of the season with Manuel Pellegrini placing both Sergio Aguero and Edin Dzeko ahead of him in the pecking order.
Both Torres and Negredo have been included in Spain’s preliminary squad for this summer’s World Cup finals, and the holders are priced at 13/2 to successfully defend the trophy.
Inter go in to the final round of league games on Sunday guaranteed of a fifth place finish.