The Australian skipper hinted a return to the side for David Warner against India.
While Warner has been recovering from a groin strain, Pucovski is battling a concussion scare.
On Warner, specifically, Paine informed he looks on track to boost the team's struggling batting unit for the New Year's Test, starting January 7.
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"David looks very good. He has started running between the wickets, so early signs with him very good for the third Test, which is awesome for us," Paine said at the post-match press conference after Australia lost the Boxing Day Test in Melbourne by eight wickets.
"Pucovski is not far away to return to play. He is pretty close to return," he added.
Australia have been missing the explosive starts which Warner provides at his best at the top as they've been failing to put the pressure back on the in-form Indian attack. After managing just 191 in the first-innings of the previous Test, the hosts were bundled out for 195 and 200 at the MCG.
Paine, however, dismissed suggestions that they need to rejig the batting order for better results in the next two games.
"Not necessarily, we need to just bat better, it does not matter who is at the crease out there," he said. "We need to be scoring runs, that's the job of the top seven in Australian cricket team."
Lack of runs aside, Paine recognised the dropped chances from his team as one other major contributor in the defeat as the visitors piled on a first-innings total of 326, guided wonderfully by their skipper Ajinkya Rahane who made an outstanding ton.
"It (low score) was one of the factors, dropping catches also did not help. It was a bit of sloppy performance in the field and not enough runs," he said.
Paine then dismissed concerns whether his team let some complacency seep into their system after the victory in Adelaide and drop their guard at training.
"(We have) same preparation for every Test. It does not change whether we win or lose. Sometimes, in international sport, the margins are very small, we can have swings in result like we have in first and second. We can minimise that, we were (simply) not at our best."
This was asked in context of the way Indians have looked well-planned to counter the hosts' two best batsmen, Steve Smith and Marnus Labuschagne. Paine, however, said their own planning hasn't been any lesser.
"India are bowling well. They have been extremely disciplined," he said. "We have not been able to get partnerships together but from what I have seen, watching Marnus and Steve Smith, this is not the first time teams have targeted the stumps. That happens every single Test match."
Labuschagne in the first-innings with 48 was the highest Australian individual score of the Test match where they collectively failed to aggregate 400 runs.
The longstanding batting issues have been exposed further through the problems faced by Smith in getting going at the start, especially while facing off-spinner Ravichandran Ashwin, who seem to have a mental wood over the great batsman.
Smith has admitted he is letting Ashwin "dictate terms" at the crease. It is felt the right-hander can be more attacking against the incisive offie. Paine, though, opined he wouldn't like to make any such suggestion to his experienced teammate.
"That's the game. Everyone is going to do it differently. Everyone has own plans," he signed off.
(Inputs from PTI)