The out-of-favour left winger has made just two league appearances for Jorge Jesus's side this season, and the report claims Liverpool and Ajax are monitoring developments closely.
Brendan Rodgers is looking to add to his attacking options in the winter window, with below-par contributions from Raheem Sterling, Iago Aspas and Luis Alberto masked by impressive goal tallies for Luis Suarez and Daniel Sturridge.
Victor Moses, on loan from Chelsea, is unlikely to make his switch permanent, which means the Liverpool boss is having to look elsewhere to supplement his attack long-term.
Ajax reportedly want the Dutch international on loan, and are keen to bring him back to the Eredivisie as soon as possible.
The former-Twente star has one cap for the Netherlands but has failed to shine since his move to Portugal in the summer of 2012.
He was initially bought for €9m, a fee which eventually rose to €12m, and his Benfica contract includes a €45m buy-out clause.
Liverpool are unlikely to have to pay anywhere near that figure, with the Dutch winger largely on the margins of the Benfica first-team since his transfer.