Smith, who led the team for nearly three years, was stripped of the captaincy and banned from leadership roles for two years in the wake of the Newlands ball-tampering scandal in 2018.
Smith's leadership ban expired last March but he has since been overlooked for roles in the Test and white-ball teams.
"If Steve Smith wants to captain Australia, I think he should captain Australia," Queensland captain Khawaja told reporters in Brisbane on Friday.
"He's our number one batsman, he's done it before, he's paid for his mistakes, there's no reason why he shouldn't be in line for the captaincy if wants to do it."
Paine succeeded Smith as captain and led Australia to their Ashes triumph in England in 2019 and briefly the top of the Test rankings
But his leadership was criticised at times during the series against India and Australia's 2-1 loss on home soil against the injury-ravaged tourists turned the spotlight on him although national selector Trevor Hohns said his position was "never in question."
Fast bowler Pat Cummins is vice-captain of the Test team and Marnus Labuschagne is regarded by some as a candidate for the captaincy despite no experience at professional level. Cummins has recently been made captain of the New South Wales one-day side.
Smith, who won a third Allan Border Medal as the country's top male cricketer, said last month the captaincy was "not on [his] radar" and the decision was out of his hands.
Various people have talked of a "process" that needs to be gone through before Smith can be considered for the role again.
Paine recently said he was sure Smith would like another crack at the job. "There's no doubt he would like to do it, I think, but we'll just wait and see what happens in the next six to 12 months," he told SEN radio. "One of the things we're trying to do is develop more leaders in our team and Steve Smith is certainly one of those."
Unless England win the final Test against India to level the series, which would allow Australia to sneak into the World Test Championship final, they will not play Test cricket again until the end of the year following the postponement of the South Africa tour.