Sky sources have said no fee has been agreed.
Earlier on Tuesday, Sky in Italy claimed a fee of 70m euros had 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.
Sky sources had previously indicated Liverpool had no plans to bid for Alisson this summer, but that was earlier in the window when the Premier League believed the Brazil international was going to Real Madrid.
Real may still be a player in the deal as they are reportedly interested in Chelsea ‘keeper Thibaut Courtois, which would mean Chelsea would be in the market for a new stopper.
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.
Alisson played five times for Brazil at the World Cup in Russia where his side suffered a quarter-final defeat to Belgium.