The midfield duo have been linked with Manchester United, but Anfield boss Brendan Rodgers is keen to beat the Red Devils to their signatures, according to The Mirror.
Rodgers, who has a sizeable transfer kitty at his disposal following Luis Suarez's big-money move to Barcelona, is also said to be plotting summer swoops for Loic Remy of Queens Park Rangers, Swansea City's Ben Davies and Southampton defender Dejan Lovren.
"We are working hard behind the scenes to find players, but it will not be a direct replacement [for Suarez]. We are looking for several players who can add to what we have and improve us again," said Rodgers.
"Obviously, Luis going gives us the clout to go and spend more and we are getting the right type of player in.
"We certainly won't spend just for the sake of spending. It has to be the sort of player who is going to improve us. But we will definitely be stronger this season - no doubt."