The Mirror says City boss Sven Goran Eriksson is eager for reinforcements up front with Rolando Bianchi proving a disappointment after a bright start.
Rising Italian star Valeri Bojinov is still sidelined, while Emile Mpenza has not proved as prolific as Eriksson had hoped he would be.
The Hammers, Cisse's other suitors, want to improve their strike force in a push for Europe.
Cisse hit 26 goals in 38 games for Auxerre before Liverpool bought him for £14million in 2004.
He never quite lived up to that price tag in a career at Anfield which was badly hampered by a twice-broken leg, but is believed to be keen to return to English football and show his full potential.