The 19-year-old striker has returned with eight goals from his 18 appearances this season, catching the eye of Reds boss Brendan Rodgers.
The report casts fresh doubt on the future of Fabio Borini, who has struggled to make an impact at Anfield following his £10.5m arrival from Roma.
Inter Milan have also been linked with a move for Icardi, who has five caps for Argentina's Under-20s side.
However, Blucerchiati director Rinaldo Sagramola has said that any potential deal is still a long way off.
The teenager has been offered a new contract at the Stadio Luigi Ferraris.