The Reds boss wants to wait until deciding to sell the midfielder.
Liverpool manager Juergen Klopp after the match
The Reds boss has been busy in the summer transfer window so far, bringing in no fewer than seven new signings.
He has also overseen a raft of exits, with Jordon Ibe, Brad Smith, Martin Skrtel and Joe Allen among several other departures.
Liverpool's Lucas Leiva in action with Wigan's Jason Pearce
Lucas was expected to be among those leaving given the fact he currently finds himself down the pecking order at Anfield.
That is a situation that is unlikely to change next season given the numerous options that Klopp has available to him in midfield.
Liverpool's Lucas Leiva in action
However, according to the Liverpool Echo, the German boss is unwilling to sanction an exit for the Brazilian until he has sufficient defensive cover heading into the new season.
The Reds defensive options have been depleted after injuries to Mamadou Sakho, Joe Gomez and Joel Matip so Klopp is in no rush to offload the 29-year-old just yet.
Instead, he will wait until later on in the window to assess his options before deciding whether or not to sanction a sale.
Liverpool manager Juergen Klopp watches the players warm up