Amid reports that many Australian team members are vouching for stand-in skipper as a permanent choice after the 50-over showpiece event, Clarke said that he has no problems with Smith as captain.
"Most definitely I would," Clarke replied on being asked on Triple M radio if he would play under Smith's leadership.
"I feel for Smithy because I sat in his shoes when a lot of the media were calling for (former captain) Ricky Ponting (to go). It's certainly not personal between Smithy and I. We've been friends for a long time and we'll continue to be," he added.
There were also reports that many Australian cricket officials are also mulling for a change of guard after the World Cup ends and Clarke believes it's best to leave all these matters to the concerned authorities.
"The people that sit above both him and I will make their decisions," Clarke said.
"Whatever they feel are the best 11 players, they will pick that 11. Whoever they feel is the best captain for the team then they'll pick that," added the 33-year-old batsman.
Clarke though did rubbish rumours about certain team member's liking Smith over the injured captain.
"I'd like to know where it's coming from. It's obviously disappointing because I haven't been around the team for the last seven weeks now I've been away from the group.
"I feel like my relationship with Cricket Australia , especially my teammates, is exceptional. I speak to all my teammates regularly," he said.
Clarke was forced to bow out after the first Test against India in December with the serious hamstring injury, and Smith filled in as captain for the three remaining Tests.
Cricket Australia has given Clarke, who hit a strokeful 51 for his local Western Suburbs team on Saturday in his first comeback game, time until Australia's second pool match against Bangladesh on February 21 to prove his fitness for the World Cup.
Clarke is now set to play for a Cricket Australia XI in a practice one-dayer against Bangladesh in Brisbane on Thursday.