The Anfield club were forced to issue a "not for sale" statement on Friday but as we know every player has his price and Liverpool think Suarez's should be a big one.
It had been speculated that Suarez had a £40m release clause but it now appears that such an amount only means Liverpool have to begin negotiations with the bidding club but they are not obliged to sell him at that price.
Instead they will seek a much higher sum for their most prized asset with the Times says they will "seek a club-record transfer fee in excess of £50 million" for the striker.
Suarez's statements that he is a keen on a move to Real Madrid while on international duty have so angered senior figures at Anfield that they are determined to call all the shots over his future.
"If anything, the events of recent days have hardened Liverpool’s resolve not to allow Suarez to engineer a move on his terms," the Times says.
"Furthermore, their belief that the Uruguay striker is one of the world’s outstanding players and at the peak of his powers means they will pursue a transfer fee in keeping with his standing if they allow him to leave."
The record sale for a Liverpool player was the £50m they received from Chelsea for Fernando Torres and Liverpool would want more than that for Suarez who they consider a superior player.
Liverpool would hope that a bidding war might open up for Suarez, but even if Real remain the only suitors "Liverpool’s present stance is that they will not even consider doing business unless they achieve what they perceive to be Suarez's full market value," reports the Times.
To other rumours and Barcelona's striker David Villa is definitely coming to the Premier League this summer, according to the Daily Mirror, with Arsenal, Tottenham and Liverpool all keen.
Wayne Rooney has been told by Paris Saint-Germain that he can name his terms for a £30 million move to France this summer – with the club ready to pay him £300,000 a week after tax. (Daily Express)
Real Madrid want Gareth Bale to submit a written transfer request to Spurs and force through an £80 million move to the Bernabeu. (The Sun)
Roberto Martinez could be offered a job at Manchester City if he loses the race to become Everton’s new boss. He is a shock candidate to be No 2 for incoming City manager Manuel Pellegrini, who is tipped to take charge next week. (The Sun)
Phil Neville is being lined up by Brighton and Hove Albion as a potential successor to Gus Poyet, with the Championship club understood to be taking steps to appoint their next manager. (Daily Telegraph)
Newcastle have told Russian rich boys Anzhi Makhachkala they will have to pay £25million to land striker Papiss Cisse. Anzhi are planning to hit Toon with a £15.4m bid for the Senegal hitman. (The Sun)
And finally Chelsea teenager Kyle Scott is wanted by Juventus, Barcelona and Real Madrid. The central midfielder, 15, is yet to sign professional forms at Stamford Bridge and Europe’s elite are keen to tempt him away. (Daily Mail)