The US Economic Envoy to Northern Ireland, Declan Kelly has welcomed Allen and Overy's move.
BBC: Law firm Allen and Overy creating 300 jobs in Belfast
But Mrs Foster said Allen and Overy had to satisfy the government agency that it had met its conditions.
BBC: Arlene Foster defends cash grants to Allen and Overy
Allen and Overy's managing partner Wim Dejonghe told the Lawyer magazine that cost savings were not the only consideration in the decision to move.
Allen and Overy has told staff that its aim is "to pass any financial benefits received from the government" to those who take up the offer.
Allen and Overy is offering staff in London first refusal on filling the jobs and if they choose not to relocate, they face losing their jobs.
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