This is according to Barcelona-based newspaper Sport, who understand that Liverpool now hope to convince the Spain international to come to Anfield as a replacement for Raheem Sterling.
The Reds generated €70 million (£49 million) from the sale of the England international, who completed his move to Manchester City earlier this week.
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It was reported last weekend, by the same publication, that Chelsea had successfully convinced the 27-year-old to join the Blues following conversations with both Jose Mourinho and Cesc Fabregas.
But the fact Chelsea only want to pay around the €20 million-mark for the World Cup winner, who has also been linked with Arsenal, means Liverpool are now the potential suitors leading the race for the winger’s signature.
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Pedro could win more trophies at Chelsea
However, whether Pedro would be prepared to swap Barcelona for a club not competing in the Champions League is unclear.
At Chelsea, he would stand a far better chance of adding to his extensive collection of winners’ medals, while Liverpool are in the process of rebuilding following the departures of Luis Suarez, Steven Gerrard and Sterling over the past 12 months.
Liverpool have already spent a significant amount of money on new recruits this summer, as the under-fire Brendan Rodgers attempts to get his team back into the Champions League at the first time of asking.
Rodgers will be acutely aware that he could be sacked if Liverpool are not on course to qualify for the Champions League around November or December.
Arsenal, Chelsea, Manchester City and Manchester United have all strengthened in recent weeks, so it will not be easy for Liverpool.
Rodgers has already strengthened his squad
But Rodgers has already signed Adam Bogdan, Danny ings, James Milner, Roberto Firmino and Nathaniel Clyne this summer. Talented Belgian striker Divock Origi is also now part of the Reds’ squad, and the 20-year-old will be joined in the coming days by his compatriot Christian Benteke after Liverpool agreed to pay the Aston Villa striker’s £32.5 million release clause.
Pedro wants first-team football, so Liverpool would need to make room for the Spaniard in their starting line-up if they are serious about bringing him to Anfield.
The player is unhappy at Barcelona, despite signing a contract extension last month, due to the intense competition for places.
Following the exploits of Lionel Messi, Luis Suarez and Neymar last season - Barcelona won an historic treble - Pedro knows his first-team opportunities will continue to be limited if he stays put.
Liverpool fans: would there be room in your starting line-up for Pedro next season? Would he flourish at Anfield? Have your say by leaving a comment in the box below!