Hayward reportedly held talks with Mohammad bin Zayed al-Nahayan, Abu Dhabi's crown prince, where they discussed the possibility of the oil-rich emirate taking a 10 per cent equity stake in BP.
The Abu Dhabi Investment Authority (ADIA), a sovereign wealth fund owned by Abu Dhabi, is considered the world's largest sovereign wealth fund with assets of more than $600bn.
An ADIA spokesman declined to comment on Hayward's meetings from which journalists were barred access.
BP shares have lost about half their value since the Deepwater Horizon oil rig exploded in April, causing the worst offshore oil spill in US history.
"It's obvious the Gulf sovereign funds are interested in BP," Ibrahim Khayat, a Dubai-based analyst, said.
"It's an opportunity not to be missed, especially as the group's current financial difficulties do not put into question the strategic value of its assets around the world," Khayat said.
Saud Masud, from the UBS financial services group in Dubai, said that Middle Eastern funds traditionally make long term investments "especially in developed markets when stocks can be picked up at large discounts".
The Kuwait sovereign wealth fund, which holds a 2.8 per cent share in BP, ruled out an increase in its holdings in BP.
"We are not currently considering increasing our stake in this company," an official of the Kuwait sovereign wealth fund said.
In Saudi Arabia, the economic daily Al-Iqtissadiya said that Saudi investors were in London for direct negotiations with BP on a possible 10 to 15 per cent share ownership.
BP has said that it can cope with the soaring costs from the oil spill without having to ask existing shareholders for cash, but the company has also indicated that it would welcome new shareholders.
The company has spent about $3,12bn towards the oil spill clean up.
BP agreed last month to create a $20bn fund for costs arising from the spill and is selling non-core assets to raise $10bn.
The head of Libya's National Oil Corporation (NOC) said on Tuesday that BP was an "opportunity" for investors, after the company's shares fell in value by half since April.
"BP currently represents an opportunity for any investor," Chokri Ghanem, NOC president, said.
"It is a recommendation that could be worthwhile for Libya or any other country or investor."