Lazio could sell right-back Massimo Oddo during the January transfer window, and they have lined up Motta as his replacement.
Marco Motta said: “To be approached by a big club like Lazio gives me great pleasure.
“I don’t know what will happen. For now I am a Udinese player, but to work again with (Lazio coach) Delio Rossi would be great as he gave me my Serie A debut.”