The Anfield club have already landed Jordan Henderson this summer and are expected to complete a deal for Blackpool captain Charlie Adam.
Less than a year after his £10million arrival from Porto, Meireles could consequently be sacrificed in order to make room in Kenny Dalglish's squad.
Liverpool are said to have told Juventus that they can have the Portugal playmaker for £13million, and the Italian club are understood to be prepared to offer Melo and cash.
The defensively-minded Brazilian has been linked with Arsenal in the past, but he is disappointed at suggestions he could be a makeweight in any Meireles move.
"Let us say that Juve are not respecting me, or at least that's the impression I get," he is quoted as saying in the Daily Mirror.
"I'm not just anyone. I'm not a bargaining chip to be used."