Malinga was released by Mumbai Indians ahead of the mega-auction earlier this year and went unsold. Following that, he joined the Mumbai camp as a coach.
However, he made a successful return to international cricket and is now eyeing a place in the Lanka squad for the World Cup next year.
England's Sam Curran and Chris Woakes, Australia's D'Arcy Short and Shaun Marsh, South Africa's Colin Ingram, Sri Lanka's Angelo Mathews and the New Zealand pair of Brendon McCullum and Corey Anderson will join Malinga in the Rs 2 crore base-price club.
India's Jaydev Unadkat, who was released by Rajasthan Royals, has listed himself for Rs 1.5 crore -- which is the maximum base price for an Indian.
Finch was released by Kings XI Punjab while Delhi Capitals (Daredevils) decided to let go of Maxwell ahead of the auction.
Their absence from the auction could also come because of the fact that the Australian Cricket Board has asked their players to return home early to prepare for the World Cup, starting on May 30.
Same goes for other board as well barring New Zealand and West Indies, who have given permission to their players to play the entire 12th season of the IPL 2019.
Players who will be a part of England's squad for the World Cup have been requested to report home by April 25 while South Africans have been asked to join a preparatory camp by May 10 while Sri Lankans are scheduled to join on May 6.
Bangladesh players and Ireland players have also been asked to head back home by April 15 and April 30 respectively.
A total of 1003 players have registered themselves for the 70 spots available in the eight IPL franchises for the upcoming mini-auction on December 18 in Jaipur.
While the newest addition are players from the Northeastern states, Uttarakhand and Bihar, there will also be 232 overseas players, who have thrown their hat in the ring. There are 800 uncapped players with 746 being Indians.
Among the foreign players, 35 Australians have registered themselves while 27 players are from Afghanistan. The highest number of players registered -- 59 -- are from South Africa while USA, Hong Kong and Ireland have one player each in the initial list.
(With inputs from PTI)