Tony Blair met Hamas leader Khaled Meshaal twice in Doha to discuss ways to end the Gaza siege, the Middle East Eye website has reported, citing unnamed sources.

The website reported on Monday that the pair last met prior to Blair stepping down from his post as the representative of the Quartet of Middle East power brokers in May.

It was reported that they discussed ways to end the Gaza siege, including the possibility of a rolling ceasefire, and that Blair's negotiations were being supported by the UK, the United States and the European Union. Two Arab states and Israel were also reportedly aware of the discussions.

Though Blair has stepped down from his post with the Quartet, the discussions are reportedly continuing.

Neither the recognition of Israel, nor the decommissioning of Hamas' arsenal, would be a requirement for any potential deal, the website reported.

When Blair stood down last month, a close source said the former British prime minister would continue to "concentrate on strengthening relations between Israel and the wider Arab world", focusing more on regional diplomacy.

Blair also planned to "focus on encouraging Israel to take measures to dramatically improve the daily lives of Palestinians in Gaza", where 2,100 Palestinians, 67 Israeli soldiers and six civilians died and thousands of Gaza homes were devastated in last year's war, the source said at the time.