Suarez, 26, has been training alone after attempting to engineer a move away from Anfield this summer.
29 May: Drops a big hint that he wants to leave Liverpool after saying he finds life in England hard.
8 July: Liverpool turn down a £30m bid from Arsenal.
24 July: Arsenal offer £40,000,001 for Suarez, triggering a clause in his contract.
2 August: Says he will consider a formal transfer request and the possibility of court action if his Liverpool dispute is not resolved.
7 August: Suarez says he wants to leave Liverpool to join a Champions League side.
8 August: Told to train alone by manager Brendan Rodgers, who says the player has shown "total disrespect" for the club.
"Initially there will be a recognition that [there needs to be] an apology to his team-mates and the club," said Rodgers when asked what the striker needs to do next.
Arsenal have had two bids rejected for the Uruguayan.
"I have seen him over a period of time. I know it is not the Luis Suarez we know and I have to protect the fans and the players because they deserve more than that," added Rodgers.
The Liverpool boss was speaking after his side, without Suarez, lost 1-0 to Celtic in their final pre-season friendly.
"He has spent some days working on his own," said Rodgers, who will be without Suarez this week as he travels to Japan with Uruguay. "The group has been separate to that and working very hard.
"When he is back from his international trip we will assess it from there."
The latest blow to Suarez's hopes of concluding a move away from Anfield comes just a day after the Reds boss urged him to accept that he is going nowhere.
"There will come a point where he'll recognise the club is not going to sell," Rodgers said on Friday.
There has been no further move from Arsenal since they bid £40,000,001 for the former Ajax striker on 24 July.
December 2011 - Given eight-match suspension and fined £40,000 for racially abusing Manchester United's Patrice Evra.
February 2012 - Refuses to shake hands with Evra at Old Trafford and is described as a "disgrace" by Sir Alex Ferguson.
October 2012 - Accused of diving by Stoke manager Tony Pulis.
November 2012 - Accused of stamping on Dave Jones by Wigan manager Roberto Martinez.
January 2013 - Mansfield chief executive Carolyn Radford says Suarez "stole" their FA Cup tie when he scored after using his hand.
The Gunners expected the bid to trigger a release clause in Suarez's contract, but his club insist it does not do so.
Suarez then told both the Guardian and the Daily Telegraph he had been promised he could leave Liverpool this summer if they did not qualify for the Champions League.
Both Rodgers and club owner John W Henry dismissed the claims.
Suarez was banned for eight matches in December 2011 after the FA found him guilty of racially abusing Manchester United's Patrice Evra and is currently serving a 10-match ban for biting Chelsea's Branislav Ivanovic.
"There are sections of fans who are unhappy with him and if he stays he will have to apologise to them," said Jim Boardman, a contributor to the online fanzine Anfield Wrap.
"I am sure he can say he's sorry and make it sound like he genuinely means it."
Liverpool boss Brendan Rodgers has told striker Luis Suarez he must apologise for his recent conduct.