The Spain international would cost in the region of £15 million and Sevilla are said to be keen for a quick sale to ease their financial problems.
In his four seasons at Seville, Negredo has scored 65 goals in 150 games across all competitions, including 11 in 12 so far this season.
He is said to be energetic, quick and an accomplished finisher both on the ground and in the air, Negredo has also been recognised by national team manager Vicente del Bosque.
He has to date won 12 caps and scored six goals though he lies behind David Villa and potential Chelsea strike partner Fernando Torres in the pecking order.
Rafa Benitez is desperate to beef up his attack in the transfer window, with Daniel Sturridge set to join Liverpool in January which will leave Fernando Torres as the only recognised forward left at Stamford Bridge.
Negredo would also add to the growing Spanish contingent at Stamford Bridge which currently includes Torres, Juan Mata, Oriol Romeu, Cesar Azpilicueta and Benitez.
Here are some highlights of Negredo in action: