Football's governing body told Reuters that all Caribbean Football Union (CFU) member associations had been given 48 hours to "provide and report all relevant information in their possession" about the meeting in Port of Spain on May 10-11 where Bin Hammam was alleged to have offered votes for cash.
"Following this 48 hour period, the ethics committee will be asked to open the necessary ethics proceedings," FIFA told Reuters in an email on Tuesday.
"Truthful and complete reporting will be considered in mitigation by the ethics committee when deciding on potential sanctions.
"Any person who has relevant information but does not come forward during this 48 hour period will be subject to the full range of sanctions."
The announcement came after ethics committee acting head Petrus Damaseb, who announced Bin Hammam's ban on Saturday, recommended investigations "into conduct of others who attended the meeting of 10-11 May."
CFU officials Debbie Minguell and Jason Sylvester were given one-year bans for their role in the meeting while former CONCACAF president Jack Warner, also placed under investigation, resigned last month.
Under FIFA statutes, this led to the investigation against Warner being dropped and the former FIFA powerbroker presumed innocent.
Bin Hammam, the former head of the Asian Football Confederation (AFC) and FIFA Executive Committee member, was found guilty of breaking seven articles of FIFA's ethics code, including bribery, after some federations, including Bahamas, Puerto Rico and Suriname, said they were offered money at the meeting.
He withdrew from the FIFA presidential election on May 29, allowing Sepp Blatter to be re-elected unopposed for a fourth term three days later.
A preliminary report by the ethics committee in June said: "The comprehensive, convincing and overwhelming evidence permits to conclude prima facie that the accused [Warner] has initiated and arranged a special meeting of the CFU member associations for Mr Bin Hammam."
"Furthermore on the occasion of this meeting it seems that Mr Bin Hammam offered, at least indirectly and under the pledge of secrecy, to each of the member associations an envelope containing $40,000."
FIFA also rejected Bin Hammam's call to make the evidence against him public.
"Mr Bin Hammam is in full possession of all evidence on his case," said FIFA.
"As is usual practice, FIFA does not make any motivated decision or any parts of the file public. This is confidential information provided only to the parties involved."
It confirmed that Bin Hammam could only launch an appeal after receiving the full written decision.
"An appeal is possible only once the motivated decision has been notified to the relevant parties [within 10 days after receiving the motivated decision]," said FIFA.
Bin Hammam has said he will appeal, describing the case against him as bogus.
The CFU is a sub-division of CONCACAF, the North, Central America and Caribbean Confederation, and has 30 affiliates, five of which are not FIFA members.
