The Social Democratic Party recently announced Alekna would join their ranks, but the athlete soon denied the information.
Alekna won gold medals in the discus throw in 2000 Sydney Olympics and 2004 Athens Olympics. He was also world champion in 2003 and 2005.
Ramūnas Karbauskis, leader of the Peasant and Greens Union, says he has spoken with Alekna, but did not discuss specific plans of him joining the party's electoral list.
"I had the opportunity to meet Alekna. He is a great person, but there is no basis to talks that he could run for elections with our list," Karbauskis said, adding that Alekna's views on healthy living was very much in tune with the party's and that he would welcome the athlete.
The Liberal Movement, too, has been trying to lure him.
"So far, we have not reached any agreements with Alekna. There have been talks, but he is still thinking over our proposals," Liberal leader Eligijus Masiulis has told 15min.lt. "We spoke several weeks ago and agreed to come back to it in May."
Alekna himself does not reveal his plans either.
"I cannot comment anything. Right now, I have not made up my mind whether I will go into politics at all," he said.
Alekna is currently working as adviser on sports at the Ministry of the Interior.
Previously, he was a bodyguard to former prime minister and late Social Democrat leader Algirdas Brazauskas. Alekna and Brazauskas, who passed away in 2014, were also personal friends.