The New Delhi Municipal Council had proposed in April that Teen Murti Marg and Teen Murti Chowk be renamed Haifa ahead of Modi's visit to Israel, the first by an Indian prime minister.
"No final call has been taken on the proposal yet. It was deferred in the April meeting and has not been taken up since then. We are not sure whether it will be scrapped totally or reconsidered later," NDMC Vice Chairman Karan Singh Tanwar told PTI.
The proposal has not been taken up in any council meeting since then.
The prime minister, who is on a three-day visit to the Jewish nation, will be visiting Haifa to pay homage to Indian soldiers who fought in the World War I.
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The Israeli city was liberated from Ottoman occupation by Indian soldiers during the war.
A large number of Indian soldiers of the 15th Imperial Service Cavalry Brigade died during the battle to free the city and nearly 900 are buried in Israel.
Demands to rename Teen Murti Road and Chowk have been made over the past few years by different organisations, including the RSS.
Senior RSS functionary Indresh Kumar had said in 2015 that the government should acknowledge the role played by the three regiments of the Indian Army in the Battle of Haifa in 1918.
According to the Ministry of Culture, a "wrong impression" has been built about the Teen Murti Chowk that it has something to do with Mahatma Gandhi.
Teen Murti Bhavan, the residence of India's first prime minister Jawaharlal Nehru and now a museum, is at the Teen Murti crossing.