However, Sky in Italy claim that a fee of 70m euros has been offered by Liverpool, although Roma want closer to 75m euros (£66.6m) to complete the deal, and that talks between the two sides are ongoing.
Sources close to Liverpool have told Sky Sports News that there has been no bid and no approach for Alisson.
Sky sources have previously told us that Liverpool have no plans to bid for Alisson this summer.
The 25-year-old made 49 appearances for Roma last season as he helped the Serie A side reach the semi-finals of the Champions League where they lost 7-6 to Liverpool over two legs.