The former France forward says he has no reason to move away from West Brom, while boss Pepe Mel does not expect him to leave and has no concerns about the striker's mindset.
The 34-year-old took to Twitter to confirm approaches from an unconfirmed number of clubs, including the Serie A side, but said he has no reason to leave the Hawthorns.
Anelka will contest an FA charge over his controversial 'quenelle' gesture in February, and Baggies boss Pepe Mel does not expect the striker to depart before the end of the transfer window on Friday.
"Thanks to Lazio & all the others clubs who wanted to sign me this last days [sic]. See you this summer if I decide to continue..." the former France international tweeted. "But the question is why should I leave my club & England? I'm happy here & I did nothing wrong...
"So now it's time to stay focus [sic] on my football with my club & I will try my best on the pitch like I always do!"
Mel, speaking at a news conference ahead of Wednesday's game against Aston Villa, insisted that the club has not told him about the possibility of selling or loaning out Anelka.
"The only thing I can say is that club has never told me that Anelka is going to leave, and that they believe he is able to play in the next five matches," he said. "Anelka wants to help West Brom win the game against Aston Villa. I think he is a player that has already shown, against Everton, that he does not have any problems. The important thing for me as manager is his performance on the pitch.
"Only [Stephane] Sessegnon is injured, the rest are available, and Anelka played well against Everton. He has a 99 per cent stage of playing [against Villa]."