"The club have now been given permission by Ajax to discuss personal terms with the player and his representatives," Liverpool said in a statement on their website.
If terms are agreed, the 24-year-old Suarez would be a welcome addition to a Liverpool team who have been enduring a poor season that has just begun to show signs of improvement after Kenny Dalglish was appointed manager earlier this month.
Torres has been somewhat out of sorts this term and the addition of Suarez, who has scored 111 goals in 159 matches for Ajax since joining in 2007, could sharpen their attack.
"I can understand Luis wanting to go to Liverpool, it's a beautiful club, but then it has to be satisfying for both parties," Ajax manager Frank De Boer said before his club released a statement along the same lines as Liverpool's.
"The departure of Luis will be a big loss but on the other hand we have the quality to win matches without him." Suarez has just finished serving a seven-match ban for biting PSV Eindhoven's Otman Bakkal on the shoulder in a league match in November.
Further controversy came at last year's World Cup when Uruguay went through to the semi-finals after his deliberate handball in the final minute of extra time against Ghana prevented a decisive goal from Dominic Adiyiah.
Suarez, who blocked Adiyiah's attempt with two hands on the line, was sent off but his team won a penalty shootout.
The striker, who has scored seven league goals this season, would join Liverpool with the 18-times English champions sitting seventh in the Premier League table.
