The Daily Express says the Reds are dealing with the fallout of the third such incident of the 27-year-old's career.
According to reports, Liverpool owner John W. Henry and other members of the club's board will speak with manager Brendan Rodgers in a conference call today.
Suarez's future was the subject of intense speculation even before his latest controversy, with the Spanish press ramping up talk of a move to La Liga.
However, the former Ajax striker may find Real Madrid and Barcelona less willing to shell out an estimated £80million on his services after appearing to bite an opponent for the third time in his career.
There are even suggestions that Liverpool will not defend their prized asset.
For the big stories and the banter follow us on Twitter: @tribalfootball