Lucas is closely linked with a move to Galatasaray but Klopp is not prepared to give the Brazilian midfielder the green light under the current circumstances.
Klopp is currently facing a defensive crisis with Mamadou Sakho, Joe Gomez and Joel Matip all sidelined.
Lucas is a central midfielder but he offers Klopp an additional defensive option and filled in at centre-back at times last season.
The 29-year-old is currently out injured with a hamstring strain but should return to training over the next two weeks.
Per the source, Klopp would sanction a move for Lucas if the Reds bring in sufficient cover.
Galatasaray meanwhile are prepared to offer €3 million for Lucas as they step up efforts to push through the transfer according to NTV Spor.
Despite the latest reports from Liverpool, the Istanbul giants remain confident that they will be able to sign the experienced midfielder.
Galatasaray sporting director Levent Nazifoglu told Turkish sports radio station Radyospor: “If Lucas Leiva puts pen to paper on a deal for Galatasaray it would not be a surprise to be honest.”