Sanchez, 22, is tipped as one of the best young players in the game and has attracted the interest of Inter Milan and Juventus, who are in talks with Udinese over a summer move.
However, Manchester United and City have also been linked with a move for the Chilean, although Lombardo believes he would be best to stay in Italy.
"It's true we did track Sanchez, but I think this player is more suited to an Italian club right now," City coach Lombardo told Radio Crc.
City will, instead, turn their attentions to Napoli as they have a host of stars who could move to Eastlands in the near future.
"I hope there can be some negotiations between Napoli and Manchester City, especially as I'd see one of their three forwards would really suit City," Lombardo added. "The trio of Edinson Cavani, Marek Hamsik and Ezequiel Lavezzi would bring success to any club.
"Napoli have very strong players, but I doubt they'd release Hamsik and Cavani at the same time. Manchester City are tracking many players because this club wants to do well, to win and to become the most important side in Europe. Napoli have good players, so that is why we are looking at them."
