PRWeek understands that the company is in the early stages of repitching the brief won by Frank PR last July.
Frank, which confirmed it had been invited to repitch for the work but declined to comment further, has handled a number of major releases during its stint as incumbent.
This has included work around Hitman: Absolution and repositioning the Lara Croft brand as part of relaunching the Tomb Raider series earlier this year.
Square Enix turned a profit of ¥2.6 billion (£16.4 million) in the six months to 30 September, which it credited to the success of Final Fantasy XIV: A Realm Reborn.
In its previous fiscal year it made a loss of ¥13.7 billion (£87.7 million), mainly due to "extraordinary" costs associated with a restructuring plan.
Square Enix has not responded to a request for comment at the time of publication.