Amr Darrag, a leader of the Brotherhood's political arm, the Freedom and Justice Party, said several members were relocating to "spare Qatar embarrassment", in a statement posted on his Facebook page late Friday.
Two Brotherhood officials in Qatar reached by AFP confirmed Darrag's statement.
Egypt designated the Brotherhood a "terrorist organisation" after the military ousted Islamist president Mohamed Morsi in July 2013.
Since then, the group's exiled leaders set up headquarters in several countries including Turkey, where the leadership in Doha may now relocate to.
"Some figureheads of the Freedom and Justice Party and the Muslim Brotherhood who have been requested to relocate their headquarters outside of Qatar have agreed (to do so)," Darrag said.
The Brotherhood's secretary general Mahmud Hussein, who is based in Doha, is thought to be the effective exiled head of the group after Egyptian police detained much of its leadership.
The Brotherhood is blacklisted in Saudi Arabia and the United Arab Emirates, and both countries withdrew their ambassadors from Doha partly over Qatar's support for the group.
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The conservative states of the Gulf view the Brotherhood's political Islam as a threat to their stability, while Qatar was seen to be backing the movement and other Islamists in a bid to extend its influence in the region.
With the leadership in Qatar likely to relocate to Turkey, where other Brotherhood figures are already based, Istanbul is poised to host the regional headquarters for the 86-year-old movement.
Other leaders are based in Britain, which has conducted an inquiry into the Brotherhood's alleged links to militants.
Qatar has come under tremendous pressure, mostly from Saudi Arabia and the United Arab Emirates, to stop supporting the Brotherhood and other Islamists such as the militias that have overrun the Libyan capital Tripoli.
But the decision to relocate the Brotherhood's leaders will leave an estimated dozens of Islamist activists in Doha, and does not suggest a major change in Qatar's policies, said Andrew Hammond, an analyst with European Council on Foreign Relations.
"I don't think it signals a major shift in policy, it looks like incremental concessions to placate (Qatar's) neighbours and prevent the dispute from getting out of hand," he said.
Cairo and its Gulf allies have also campaigned against the Doha-based Al-Jazeera broadcaster, whose journalists have been imprisoned in Egypt. The network's Arabic channels have strongly opposed Morsi's overthrow.
"The other issue is what happens with Jazeera's line. Does that shift? Nothing has changed so far," Hammond said.