According to a survey by pollster Mercados y Muestras on the country's news website Pagina Siete, the party founded by Evo Morales came out ahead with 23 percent of the vote.
Morales resigned on Nov. 10 following weeks of opposition protests against his re-election to a fourth term. However, he said that he is still president of Bolivia.
Morales, currently under political asylum in neighboring Argentina, has said Rodriguez, 30, "is too young to be a candidate for the presidency," the website reported.
Conservative candidate and ex-President Carlos Mesa came second with 21 percent of the vote.
In third and fourth place were Chair of the Civic Committee of Santa Cruz Fernando Camacho and President of the Potosinists Civic Committee Marco Pumari, with 13 percent and 10 percent, respectively.
Bolivia's Supreme Electoral Court has yet to set a date for the presidential election, but parties are already proposing potential candidates.