Finch will be re-assessed ahead of Saturday's training before a final call is made on his availability. The 32-year-old had suffered from a back injury during a Marsh Sheffield Shield Match, earlier this month.
However, Finch has claimed that he has almost recovered from his injury and is progressing well.
"It's still two days before the game, so I'll test it out over the next two days," Finch said prior to training today.
"But I'm feeling like it will be fine.
"It's feeling better and better every day.
"It's just going to be a case of having a hit today, assessing how it goes, having a hit tomorrow and keep re-assessing each day."
Should Finch, who lead the Aussies in the 50-overs World Cup, fails to fully recover, then Cummins would become the first specialist bowler to captain Australia in men's limited-overs cricket.
Australia squad: Aaron Finch (c), Ashton Agar, Alex Carey, Pat Cummins, Glenn Maxwell, Ben McDermott, Kane Richardson, Steve Smith, Billy Stanlake, Mitchell Starc, Ashton Turner, Andrew Tye, David Warner, Adam Zampa
Sri Lanka squad: Lasith Malinga (c), Kusal Perera, Kusal Mendis, Danushka Gunathilaka, Avishka Fernando, Niroshan Dickwella, Dasun Shanaka, Shehan Jayasuriya, Bhanuka Rajapaksa, Oshada Fernando, Wanindu Hasaranga, Lakshan Sandakan, Nuwan Pradeep, Lahiru Kumara, Isuru Udana, Kasun Rajitha