A Brotherhood official said on Saturday that several members of the group were relocating after Qatar came under enormous pressure from other Gulf Arab states to cut support for the Islamist group.
"If they make any request to come to Turkey, we will review their request," Erdogan was quoted as telling reporters on his plane back from an official trip to Qatar late on Monday.
"If there are any reasons that would prevent them from coming to Turkey, they would be assessed. And if there aren't any obstacles, they would be granted the ease that is granted to everyone," he said.
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Turkey and Qatar have been some of the staunchest supporters of the Brotherhood, the movement of Egypt's former president Mohammed Morsi who was ousted by the army last July following mass protests against his turbulent year-long rule.
But other leading Gulf states have grown increasingly concerned about the Brotherhood after its prominent role in the Arab Spring, viewing the movement as a threat to their monarchic rule.
Egypt's military-installed authorities designated the Brotherhood a "terrorist organisation" last December.
Since then, the group's exiled leaders set up headquarters in several countries including Turkey, to where the leadership in Doha may now relocate.