Australia will host the next Ashes series in 2017-18.
Former paceman Gillespie is currently coaching Adelaide Strikers in Australia's Twenty20 Big Bash League after spending five years coaching English county side Yorkshire.
"There is a national selector's job up next year and I might put my name up for that," he told News Ltd. "All I have done the last five years is select teams for Yorkshire. I wouldn't rule anything out. If there are opportunities I will look at it."
Former test captain Waugh, who announced his retirement in 2004, said he would be willing to discuss the job if an offer came his way.
"I'd listen to it if the opportunity came up, but there are a lot of things you've got to throw into the mix and see whether it's the right time," Waugh told the Sydney Morning Herald.
"I think there are a lot of good cricket brains in Australia. No one has asked me, but I'd listen to it."
Under Marsh's chairmanship of the panel, Australia lost the 2015 Ashes series in England but won the 50-overs World Cup on home soil in the same year and held the number one ranking in test cricket for six months earlier this year.
(Reporting by Ian Rodricks in Bengaluru; Editing by Peter Rutherford)
