TMW says the Reds see the former Everton attacker as a potential replacement for Mohamed Salah or Darwin Nunez.
Salah is off contract at the end of the season, while Nunez remains on the shopping list of Saudi Pro League clubs after Liverpool blocked a January move to Al-Nassr in January.
Lookman is emerging as a priority target for Liverpool and it's also been revealed he has a 'gentleman's agreement' with Atalanta owners, the Percassi family, that he will be allowed to leave this summer.
The pact was reached after La Dea lost Teun Koopmeiners to Juventus last year. Lookman agreed to stay after Atalanta's urgings as they wished to avoid losing two star players in the one transfer window.
Interestingly, along with Liverpool, Juve are also being mentioned as potential suitors for the Nigeria international.
There has been contact with Lookman's camp, but the player has insisted he wants to focus to the end of the season on Atalanta as they chase Champions League qualification and a potential Scudetto tilt.