FIFA's chief ethics investigator Michael J Garcia has closed that case after failing to uncover any new evidence.
It is a significant development in the case of Bin Hammam, who has always denied any wrongdoing, and who had a lifetime FIFA ban overturned by the Court of Arbitration for Sport in July due to insufficient evidence.
The court overturned a ruling by FIFA's ethics committee that the 63-year-old Qatari was guilty of paying bribes at a Caribbean Football Union meeting in Trinidad and Tobago in 2011.
Bin Hammam remains provisionally suspended over allegations of financial mismanagement while president of the Asian Football Confederation, but his legal team this week launched a challenge to that suspension in the Swiss courts.
Garcia's decision to close the investigation in to the Caribbean allegations is contained in his confidential report to FIFA.
It states: "This investigation focused on events that took place at the CFU meeting in Trinidad and Tobago in May 2011.
"With respect to the events at the CFU conference, the investigation uncovered no new material proof beyond the substantial evidence presented during the proceedings that culminated with the CAS decision vacating Mr Bin Hammam's ban.
"Accordingly, the Investigatory Chamber has closed this matter consistent with the CAS Panel's guidance regarding newly discovered evidence."
In July, a CAS three-man panel voted 2-1 in Bin Hammam's favour but added that his behaviour was "not of the highest ethical standard" and that "it is more likely than not" that he was the source of cash brought into Trinidad and Tobago and distributed by former FIFA vice-president Jack Warner.
CAS said then: "It is a situation of 'case not proven', coupled with concern on the part of the Panel that the FIFA investigation was not complete or comprehensive enough to fill the gaps in the record."
FIFA then appointed Garcia, a New York-based attorney, to launch a new investigation but he has found no additional evidence.