"Today a letter was sent to Israel, it's an invitation for them to join the Western European countries group," a diplomatic source told AFP.
"Now they are waiting for Israel's response," the source said.
Formally known as the West European and Others Group, the 28-nation bloc is made up of European nations, the United States, Canada, Australia and New Zealand.
Israel has repeatedly locked horns with the Human Rights Council -- a 47-nation body whose make-up rotates among members of regional groups within the UN -- accusing it of bias.
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At odds with its neighbours, Israel lacks a berth in the Asia-Pacific Group which covers Middle East nations.
Joining a group does not guarantee Israel will get a slot on the council, but nonetheless gives the Jewish state more sway than it has out in the cold.
Israel is already part of the West European and Others Group in New York -- home notably to the UN Security Council -- but had not been invited on board in Geneva where the globe's human rights bodies are located.
After the council launched a new probe of its record, Israel opted to boycott the UN body in March 2012.
In January this year it became the first country to refuse to attend a review of its rights record -- something all UN members are meant to submit to regularly.
In October, however, Israel changed tack and sent a delegation to its rescheduled review.