The 29-year-old wants to quit La Liga after two years in Spain and his agent Christophe Magoui told BBC Sport Kanoute wants to move back to England.
Magoui said: "We have interest from the three Premiership clubs but have not had a firm bid from any as of yet.
"But Fredi wants to leave Sevilla and his first choice destination in England and the Premiership."
Kanoute left England in August 2005 after successful spells with West Ham and Tottenham.
He struggled at first in Spain but has just enjoyed a fabulous season at the Ramon Sanchez Pizjuan, scoring 21 goals in the league as Sevilla finished third and retained the Uefa Cup.
Magoui says Kanoute will not stay in Spain and could link up with his former Hammers boss Harry Redknapp at Portsmouth.
"Would Fredi want to link up again with Harry? Sure, why not?" added Magoui.
"No clubs in Spain have registered any interest in Fredi but he has made up his mind that he wants to return to England anyway.
"The cost to sign Fredi will be £6.7m, but so far it is just interest."
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Bolton IMO do not need a striker, unless of course they have plans to sell Anelka.
The same is also true of Newcastle - it would make the signing of Viduka somewhat obsolete.
Pompey definately need someone like Kanouté though, although for £6.5m, I'm surprised that Liverpool aren't interested - just for a stop gap until they could possibly sign Villa next summer.
Is this also somewaht bizarre? that he wants to leave Sevilla I mean And he seems to be finding La Liga a breeze! Maybe he wants a new challenge, though to quit just before playing in the CL with Sevilla seems a bad decision in my books