One diplomat said his departure as Quartet envoy was “long overdue”.
According to a source in a BBC report he will leave the role next month after he fulfils "outstanding commitments.
The source said Mr Blair remains "fully committed to assisting the international community in its work with Israel and the Palestinians to bring about progress on the two-state solution.
"He believes that he can best support these efforts through working with the key regional players, the USA, the EU and others, without any formal role.
"He will also focus on encouraging Israel to take measures which will dramatically improve the daily lives of Palestinians in Gaza.
"He believes that achieving this progress on the ground is an essential prerequisite to strengthening broader Arab-Israeli relations."
