There has been no official confirmation from the Uruguay Football Federation on whether an operation will take place, but it is expected to make a statement later on Thursday.
Any surgery would likely sideline the striker, the Professional Footballers' Association and Football Writers' Association player of the year after scoring 31 league goals, for at least three to four weeks.
England play Uruguay in Group D on June 19 in Sao Paolo.
Uruguay, however, remain confident at this stage that Suarez will be fit for the tournament in Brazil.