Warne – who took 708 wickets in 145 Test matches for Australia – retired from international cricket in 2007.
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A variety of commitments have filled his time since then, ranging from Twenty20 cricket to media to professional poker, but the 44-year-old has dipped his toe in the coaching waters recently.
He worked with Australia's spinners in South Africa recently and made a brief appearance in the Proteas nets to talk with fellow leg-spinner Imran Tahir at the recent ICC World Twenty20 tournament.
Warne took charge of the ICC's official Twitter account on Sunday and was asked by a follower if he would consider being the new England coach.
"Part of me would love to put my name into the mix," Warne responded.
"But I would want KP (axed batsman Kevin Pietersen) in the team and lose 10 support staff. I could go on."
In February, Warne created speculation when he said he would "think about" taking on the England job.
He quickly backed down from the comments though, saying he was "flattered" at the attention but that his priorities were with the Australia team.
The position has been vacant since Andy Flower stepped down as England boss in January.
Current limited-overs coach Ashley Giles, former boss Peter Moores and Mick Newell have all been linked with the job but a decision is still to be made.