The 27-year-old striker has been heavily linked with a move away from the Ramon Sanchez Pizjuan this summer, having attracted admiring glances from a number of top European clubs.
Spurs boss Andre Villas-Boas has been credited with an interest in signing Negredo, as he looks to strengthen his forward line at White Hart Lane ahead of the new campaign.
Tottenham face serious competition to secure the Spain international's signature, though, after Atletico Madrid launched a £13million bid to sign him.
However, Diego Simeone must raise his offer by at least £8million if he is serious about adding Negredo to his first-team ranks at the Vicente Calderon, after their La Liga rivals raised their valuation of the player.
Negredo hit 25 goals in 36 Primera Division appearances in 2012/13, and Sevilla will be determined to keep hold of their star striker, particularly after the recent sale of Jesus Navas to Manchester City.
By increasing his asking price to around £21.5million, the Spanish club will stand a much better chance of retaining his services, as they look to deter the likes of Tottenham and Atletico Madrid from making another bid.