JERUSALEM, Jan 1 (Reuters) - The Israeli and U.S. companies developing the massive Leviathan natural gas field off Israel's coast may have to sell their stake in two smaller fields to avoid being branded a cartel by the anti-trust authority.

Delek Drilling, one of the Leviathan partners, said on Wednesday the group was in "advanced negotiations" with Israel's anti-trust authority to receive the regulator's approval for their operations in return for selling their stakes in the Tanin and Karish fields.

Tanin and Karish, which are licensed to Delek Drilling, Avner Oil Exploration and Texas-based Noble Energy , have combined estimated reserves of 3 trillion cubic feet (tcf).

That is far less than the deposits in the group's other fields -- Leviathan has 19 tcf and Tamar has 10 tcf.

The negotiations with the anti-trust authority began over two years ago, Delek Drilling said in a statement to the Tel Aviv Stock Exchange, but gave no further details. Delek Drilling and Avner are subsidiaries of Delek Group

Israel financial daily Calcalist reported that if an agreement is reached, the companies will have 2.5-4 years to sell their stakes in Tanin and Karish.

"At this stage it is only about negotiations and there is no certainty that the negotiations will lead to a binding agreement," Delek Drilling said.