Mr Burke and shadow treasurer Joe Hockey have spent the last two years debating on Seven's Sunrise in a regular Friday spot.
But as of Friday, former prime minister Rudd replaces Mr Burke on the show.
The environment minister says he enjoyed his time on the program and would love to do it again if asked.
"I suspect as a former PM, as much as I'd love to be there, I reckon he'll (Mr Rudd) beat me in the ratings," Mr Burke told reporters in Sydney.
"I wish him well.
"If the opportunity comes back for me I'd grab it."
While in opposition, Mr Rudd appeared alongside Mr Hockey on the show regularly before he successfully challenged Kim Beazley as Labor leader.