Brendan Rodgers is said to view the Belgian midfielder as the perfect signing for his side.
The Merseyside club are currently lacking attacking options after loaning Andy Carroll to West Ham United and selling Dirk Kuyt in the summer. It is thought that Mertens could add some much-needed firepower at Anfield.
Mertens, who joined PSV from FC Utrecht in 2011, is a creative outlet for the Dutch side, having notched six assists and four goals in just seven games in the Eredivisie.
It is rumoured that Kenny Dalglish wanted to sign Mertens before he was sacked in the summer. Now, it seems that Rodgers is ready to continue the pursuit.
Mertens has earned 12 caps for Belgium since making his debut in 2011.