The Italian giants, who signed Justin Kluivert yesterday for £17m, are wary of underselling the Brazil goalkeeper after parting with Mohamed Salah for a bargain £36m last summer.
Roma have valued Alisson at closer to £70m, a fee that would far exceed any ever paid for a goalkeeper.
Real Madrid retain an interest in the player but are similarly unlikely to unload such a huge amount despite Florentino Perez's keenness to address the position.
Thibaut Courtois' contract situation at Chelsea, where his deal has already ticked into its final 12 months, makes the Belgian a much more affordable target while any club willing to spend close to nine figures on a goalkeeper is likely to pay the release clause for Atletico Madrid's Jan Oblak, widely considered to be one of the best goalkeepers in the world.
Liverpool are set to look elsewhere for more reasonably-priced options in goal and are still pursuing a deal for Xherdan Shaqiri, who they believe will add depth to their attacking line.
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