The Frenchman, 34, has been linked with a move away from the Baggies after creating a media storm over his 'quenelle' goal celebration - a gesture that is alleged to have anti-Semitic connotations.
Anelka was recently charged with misconduct over the incident by the Football Association, but he denies the charge.
He tweeted: "Thanks to Lazio & all the others clubs who wanted to sign me this last days. See you this summer if I decide to continue...
"But the question is why should I leave my club & England? I'm happy here & I did nothing wrong..."
Anelka joined West Brom on a free transfer last summer.