The Spaniard looks set to leave the Nou Camp in January after growing concerned with his first-team prospects following the arrival of Luis Suarez.
At 27, the winger is keen to be playing regularly and Arsenal have bee mooted as his most likely suitors.
But Liverpool manager Rodgers is desperate to add quality to his ranks after a stuttering start to the season, and sees the La Roja ace as a wise purchase.
Reports suggest that an offer of around £25m will be needed for Pedro, and the Merseysiders are open to presenting a fee in that region after a net spend of around £30m over the summer.
Rodgers us believed to be concerned by his team’s reliance on teenage winger Raheem Sterling, who has been a shadow of the player who nearly fired the Kop side to the title last term.