The £74m buyout, which combines Gamestation's 217 stores with Game's 830 stores across Europe, is being investigated to see whether it will result in significantly reduced competition.
If the OFT rules that this is the case, the acquisition could be referred to the Competition Commission for a full review.
"The OFT is considering whether arrangements are in progress or in contemplation which, if carried into effect, will result in the creation of a 'relevant merger situation' under the merger provisions of the Enterprise Act 2002," said an OFT spokesman.
"Should it be found to be a 'relevant merger situation', the OFT will further consider whether the creation of that situation may be expected to result in a substantial lessening of competition within any market or markets in the UK."
Game has said that the OFT process is part of the "normal regulatory review" of mergers of this nature and that it "will be co-operating fully".
The OFT is currently inviting comment on the case until 14 June when deliberations will begin.
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