Smith stressed last week that Test cricket was his priority, and he was prepared to skip the T20 World Cup in October-November.
The 32-year-old had withdrawn from the ongoing white-ball tour of the West Indies due to the elbow injury.
Steve Smith reclaimed the number one position in the ICC Men's Test Player Rankings for the first time since the Boxing Day Test last year.
Cricket Australia should make ball-tampering investigation report public, says ex-bowling coach Saker
CA chief Nick Hockley had said last month that they do not intend to make the investigation report public.
If you do piecemeal probe, it will keep biting you on backside: Michael Vaughan to Cricket Australia
The trio of then Australian skipper Steve Smith, his deputy David Warner and Cameron Bancroft were banned for their roles in the ball tampering scandal.
The issue was put under the spotlight again when Bancroft last week revealed that Australian bowlers in the team at that time might have had some knowledge about the plot.
Ever since Australia lost the Test series against India, there have been calls to replace the skipper and Paine has coped with severe criticism.
Have very good captains, no position available: Australia coach Langer on Smith's 'leadership' comments
On Monday, Smith for the first time came out to talk about his keenness to lead Australia once again if given the chance.
During the IPL 2021 Player Auction last week, the runner-up of the previous season acquired the services of experienced players such as Smith and Tom Curran along with four talented domestic players.
IPL Auction 2021: Chris Morris' record deal to Cheteshwar Pujara's return, here is everything you need to know
New Zealand pacer Kyle Jamieson, who is known more for his performances in Test cricket, secured a massive Rs 15 crore deal from the Royal Challengers Bangalore.
A man who recently sold Daniel Craig's Aston Martin will be in charge and there will almost be Rs 200 crores in play. Simply put, the IPL auction is set to be another splashy affair.
Steve Smith beat Pat Cummins by 12 votes to win the Allan Border Medal, the highest honour in Australian men's cricket.
Apart from Smith, England's Moeen Ali, former India off-spinner Harbhajan Singh and Aussie Glenn Maxwell too have registered in the Rs 2 crore bracket.
The Indian spinner reflected on those achievements and spoke about what's next to select media on Sunday. Excerpts
Why Steve Smith eligible for captaincy while David Warner got lifetime leadership ban, asks Ian Chappell
Alongside vice-captain Pat Cummins, the 31-year-old Smith seemed to be a front runner if Paine is to be replaced as Test skipper as a fallout of Test series loss to India.