The 27-year-old has been a prolific scorer at the Andalusian outfit since signing in 2009, but now wants to test himself at a higher level.
Atletico have lost leading marksman Radamel Falcao to Monaco and are seeking a replacement, and Del Nido has claimed that their La Liga rivals have targeted Negredo, who is keen to move on to bigger things.
"He has said he wants to develop and that he wants to play in the Champions League," Del Nido told Sevilla's television channel.
"One of the teams is Atletico Madrid and the other is outside of Spain."
Arsenal, Napoli and West Ham United have also been linked with the forward.