The 27-year-old has been heavily linked with a move to the Premier League for some time, and came close to joining Everton in the January transfer window.
It's thought that David Moyes still holds an interest in bringing the Spain international to Goodison Park, but the Toffees are now well down the pecking order in the hunt for his signature.
Spurs boss Andre Villas-Boas is a long-term admirer of Negredo's, and was linked with him during his time in charge of Chelsea.
Roman Abramovich has continued to monitor the player's situation as he weighs up an attempt to lure him to Stamford Bridge, but will face competition from the club's former manager at White Hart Lane, as he too looks to strengthen his squad ahead of 2013/14.
Negredo has always been keen on a move to the Premier League, previously stating: "It is a league that I like and sooner or later I will play in it."
Now, Michael Laudrup is hoping to beat the likes of Chelsea and Tottenham to the player's signature, in a bid to partner the Sevilla star with his compatriot Michu at the Liberty Stadium next season.