West Ham had a bid of around £14.5m turned down by Sevilla earlier this month and they are thought to be in the hunt again, although since then they have landed Andy Carroll from Liverpool so their interest may have waned.
Negredo struck 25 goals in La Liga last season, the fourth highest in the league, but has informed the Andalusian club of his desire to move on.
"He has said he wants to develop and that he wants to play in the Champions League," Sevilla president Jose Maria del Nido told Sevilla's official TV channel.
"One of the teams is Atletico Madrid and the other is outside of Spain. Sevilla will choose the best offer."