Earlier this week, Liverpool manager Brendan Rodgers said the wantaway striker would have to apologise to the club for publically asking for a move away from Anfield before he could work again with the first team.
The Uruguay international had been made to train on his own as the Reds boss was unhappy with the attitude he has shown recently, which culminated with interviews in which he claimed the club had reneged on a deal to allow him to leave this summer.
Sky Sports News and the Guardian both reported that Suarez did indeed say sorry to his team-mates and was thus allowed to train.
In media briefings before the club's season opener against Stoke on Saturday, Rodgers insisted his side would not be distracted by the ongoing Suarez transfer saga.
Rodgers instead backed his side to put off-field issues to the back of their minds and shine on the pitch.
"There's too much good work gone on here for it to be overtaken by anything else," Rodgers said. "The players have worked so hard, their concentration has been brilliant and we are all very determined this year.
"I can't let anything detract from that. Nothing can sabotage what we are trying to do. I don't really want to go on about it. It's just something we cannot afford to happen."