The defender is currently down the pecking order at Anfield.
The Italian side are keen to add a defender to their ranks in the January transfer window to bolster their struggling defence.
The Biancocelesti have conceded more goals than other side in the top 10 of Serie A this season and are looking to fix that in the second half of the campaign.
That has led to them to exploring a number of options, and Il Messaggero claims that Liverpool’s Toure is among them.
The Ivorian defender is currently far down the pecking order at Anfield, with Dejan Lovren, Martin Skrtel and Mamadou Sakho all ahead of him.
His contract is set to expire in the summer, and after making just eight appearances so far, it seems unlikely that he will be expending his stay on Merseyside beyond the summer.
That could tempt Liverpool to sell and recoup at least something, and Lazio would be keen as they seek to add some experience to their defence after losing Stefan de Vrij and Santiago Gentiletti to injury.