Brendan Rodgers has told Luis Suarez that he is keen for him to remain at Anfield, the Mirror understands.
The Uruguay international has constantly been linked with a move away from Liverpool, with the striker repeatedly stating he desire to leave.
However, after the pair met for the first time since the end of last season yesterday, the Reds boss told Suarez that he will fight to keep him at the club amid interest from Premier League rivals Arsenal.
Meanwhile, the Gunners are set make an improved bid of £40m for the 26 year old, according to the Mirror.
That figure would reportedly trigger a clause in his contract that would allow him to speak with interested parties.
Elsewhere, the club are closing in on a loan deal for Valenica left-back Aly Cissokho, according to the Metro.
The Reds are set to pay the La Liga side an initial £900,000, and would have the option of buying the 25 year old for £3.5m at the end of the season.
Cissokho only moved to Spain last summer having spent four years with Lyon in Ligue 1, during which time he won his one and only cap for France, in a 2-1 friendly defeat to Norway back in 2010.