The Spaniard is reportedly being tracked by both Spurs and Chelsea, who have been impressed by his form in La Liga.
Sevilla President Jose Maria del Nido has reportedly travelled to London to discuss a potential move, although the club deny that this is the main purpose of his visit.
Andre Villas-Boas has targeted the 27-year-old with news that Emmanuel Adebayor will leave the club for the Africa Cup of Nations.
The Togo star’s departure leaves the White Hart Lane outfit with only Jermain Defoe as a central-striking option, a problem which is believed to have shaken AVB into action.
It was believed that the North Londoners were set to move for Internacional forward Leandro Damaio, but reports have emerged that his club are unwilling to allow him to leave this month.
Negredo is said to available for £15m, with Sevilla keen to address financial difficulties.
The Spanish international began his career with Rayo Vallecano before moving to fellow Madrid-based club Real.
He failed to make an impact on the first team at the Bernabeu, prompting a switch to Almeria, where he forged his reputation as a proven goalscorer.
A record of 32 goals in 73 appearance alerted Real, who bought him back to the club only to sell him straight to Sevilla with a buy-back clause in the deal.