The game's global governing body appears to have backtracked on earlier claims and insists the Uruguay international is not available to train but can be transferred
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However, when asked to clarify these remarks, Fifa insist Sulser was “inaccurate” and that Suarez would not be allowed to train with either Uruguay or Liverpool.
"This is inaccurate," said a Fifa spokesperson. "Claudio Sulser just said he could make the medical testing for a transfer [only this] but clearly said as many times earlier that he cannot do any football activity which includes that he cannot train with the national team nor club."
Suarez is allowed to move clubs during his ban, and Goal understands Barcelona are on the verge of signing the Uruguay international in a £70m deal.
Barca sporting director Andoni Zubizarreta has previously praised Suarez after he finally apologised for biting Giorgio Chiellini during Uruguay's clash with Italy at the World Cup.
Suarez was banned from all football-related activity for four months, banned for nine competitive international matches and hit with an €80,000 (£64,000) fine for the incident although Uruguay have appealed the ban in an attempt to have it reduced.