(Adds details on court rejecting FTC request in paragraph 4 and background throughout)

July 13 (Reuters) - Microsoft Corp and Activision Blizzard are considering giving up some control of their cloud-gaming business in the UK to appease regulators so they can complete their $69 billion merger, Bloomberg News reported on Thursday.

The deal, the largest in the history of the video game industry, was also struggling in Britain until this week. Britain's Competition and Markets Authority, which had opposed the transaction, said on Wednesday a restructured deal between Microsoft and Activision Blizzard could satisfy its concerns, subject to a new investigation.

The sale could involve the cloud-based market rights for games in the UK to a telecommunications, gaming or internet-based computing company, the Bloomberg report said, citing people familiar with the matter. A private-equity company might also be interested, according to the report.

The U.S. Federal Trade Commission (FTC) had requested a temporary halt to the deal, but a U.S. court on Thursday rejected the request.

Microsoft and Activision did not immediately respond to Reuters' request for comment.

The two U.S. companies had agreed to a deal deadline of July 18, with Microsoft liable to pay a $3 billion breakup fee if it fell through. Still, with the larger $69 billion deal back on track, the two sides are now focused on modifying the deal to obtain regulatory approval.

(Reporting by Lavanya Ahire in Bengaluru; Editing by Sherry Jacob-Phillips)