The 27-year-old scored 25 goals this season, including all four in Sevilla's dramatic final day 4-3 win over Valencia last weekend.
The Spanish club are prepared to let the forward go this summer, but only to a side that matches the £20million release clause in his contract.
Everton were linked with a move for Negredo in January but baulked at the £20million fee while Premier League rivals West Ham have also been mentioned in recent weeks.
His agent Juanma Lopez has confirmed there is interest from the Premier League for the player but hinted that Rafael Benitez's Napoli may be his preferred option.
Negredo is keen to test himself in the Champions League and Napoli's automatic qualification for Europe's premier competition next season has shot them to the head of the queue.
"Alavaro has played a very important season and many clubs are coming forward for him," Lopez told tuttomercatoweb. "I think he can go either to England or Italy.
"Napoli is a possibility given that [Rafa] Benitez likes the player and the team will play in next season's Champions League, a competition that Negredo would like to take part in.
"The final decision is up to Seville, whoever wants Negredo has to find an agreement with them."