The Reds boss was thought to have held talks with Roma director of football Walter Sabatini on his visit to the Italian capital.
Though Liverpool have begun exploratory talks over a move for Pjanic, the Daily Mirror claims the Merseyside outfit and Roma are poles apart in terms of their valuations.
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Miralem Pjanic is on Liverpool's radar
Liverpool have been quoted £37m for Pjanic, who is viewed as a long-term replacement for the departing Steven Gerrard.
The report also claims Liverpool will have to offer Pjanic a wage packet of £160,000-a-week in order to stand a chance of luring him to Anfield.
Rodgers is also thought to be interested in Pjanic's team-mates - Radja Nainggolan and Adem Ljajic.
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