The proposal moved by NPC chairman C.V.K. Sivagnanam says the memorial will be built at Nallur, where Thileepan died following 11 days of fast-unto-death, on 26 September 1987.
Sivagnanam said the column made of cement at the location is now in ruins.
Thileepan had refused to eat or drink, demanding talks between his organization and the Indian troops that were occupying the north at the time.
Born on 29 November 1963 at Urali and educated at Hindu College, Jaffna, he was a medical student when he joined the LTTE.
The LTTE gave a lieutenant colonel rank for him.