Icardi, 19, has shown a lot of potential after he was called upon to replace injured Maxi Lopez, with top Italian clubs now lining up for his signature.
Despite playing first team football at Marassi, the striker has reportedly requested a transfer and could be leaving Genoa in the January transfer window.
While Juventus, Fiorentina and Inter are all keen on the talented forward, Il Corriere dello Sport understands that Lazio are leading the race at the moment.
The Biancocelesti see Icardi as a perfect replacement for veteran striker Miroslav Klose, and believe the Argentine footballer would profit a great deal from training alongside such a quality and experienced striker.
Lazio, however, first need to get rid of two strikers before making a move for Icardi, given that Sergio Floccari, Libor Kozak and Tommaso Rocchi are all currently behind Klose in the pecking order.