TalkSPORT reports how the 27-year-old was heavily linked with a move away from the Ramon Sanchez Pizjuan during the January window, but a transfer failed to materialise.
Gunners boss Arsene Wenger had been credited with an interest in bringing him to the Emirates Stadium, while north London rivals Tottenham were also looking to strengthen their forward line, with Andre Villas-Boas relying heavily on Jermain Defoe and Emmanuel Adebayor.
Chelsea complete the trio of English parties reportedly courting Negredo's signature, although the vacant manager's job at Stamford Bridge might put the possibility of the Spain international moving to west London in doubt.
What is certain, however, is that the Sevilla hit-man - who has scored 15 goals in La Liga so far this season - has set his sights on a move to the Premier League at some point in the future, after intimating his future plans in a Spanish radio interview.
"I've always said it and I've never tried to keep it hidden," Negredo told Cadena COPE. "The Premier League is a league that I like. I don't know if it's now, maybe a bit later, or tomorrow, but I will play there.
"The president received an offer in January but he didn't look at it. They never said anything directly to me and it wasn't time to leave. I don't know what will happen in the future. It depends on what the club wants and what it needs."
Negredo is currently on international duty with Spain for the upcoming World Cup qualifiers against Finland and France, and Chelsea, Arsenal and Tottenham are likely to be watching with curiosity, as the three London clubs consider moves for the striker in the summer.