The 29-year-old wants to quit La Liga outfit Sevilla after two years in Spain and his agent Christophe Magoui told BBC Sport that 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 is England and the Premiership. The cost to sign Fredi will be £6.7million.
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 La Liga as Sevilla finished third and retained the UEFA Cup.
And Magoui admits Kanoute 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 £6.7million, but so far it is just interest."