The football governing body declared that Suarez can undergo a medical ahead of a potential transfer, as Barcelona are closing in on a 75 million-pound deal for the Uruguayan striker after negotiations with Liverpool.
According to The Mirror, previously it had been thought that FIFA meant Suarez would not be allowed to train when he returns to his Premier League side.
But, now FIFA appeared to have cleared Suarez, who was banned after his third bite on an opponent in four years, to take part in pre-season training, whether the striker is at Liverpool or at Barca.
The head of FIFA`s disciplinary committee Claudio Sulser said that one cannot limit those rights to the player, because it would be disproportionate.
Uruguay have also launched an appeal against the ban, which rules the Suarez out of their next eight fixtures thus effectively ruling the striker out of next year`s Copa America, the report added.