Vaughan missed the whole of England's international series in India when his longstanding knee problem flared up again and that led to suggestions the 31-year-old could stand down from limited overs cricket in order to extend his Test career.
The Yorkshire batsman himself was the beneficiary of such an arrangement when he captained the one-day team after Nasser Hussain quit leading England in the shorter form of the game after the 2003 World Cup, a move that paved the way for Vaughan to also take over as Test captain later that year.
However, Graveney said fresh talk about two permanent captains was not something on his agenda or that of England coach Duncan Fletcher.
"It hasn't been a subject that has cropped up in my discussions - which have mainly been about support for Vaughan - or whatever discussions I've had with Duncan when I've made contact with him in India."
After regular vice-captain Marcus Trescothick also came home early from India, all-rounder Andrew Flintoff led England to a highly creditable 1-1 draw in the Test series before the side went down 5-1 in the one-dayers.
Andrew Strauss, who has captained Middlesex, also filled in as skipper when all-rounder Flintoff was rested to extend England's leadership options in the event of a permanent vacancy.
Vaughan, while making it clear he wanted to continue as both Test and one-day captain, said last week: "In the future if a stage comes whereby missing out on one form of the game will prolong my cricket for a few years then, of course, that decision will be made."
England were without several key players in India because of injury and some of those star names could yet be out of action come next month's first Test against Sri Lanka at Lord's.
As well as Vaughan, it looks as if England will be without left-arm spinner Ashley Giles, yet to to start running again following his hip operation before Christmas, and fast bowler Stephen Harmison, who missed the one-day series in India with a shin problem.
But Trescothick (virus) and paceman Simon Jones (knee) are both hopeful of being available after lengthy spells on the sidelines.
And with an Ashes tour and World Cup on the horizon, not to mention home Test and one-day series against both Sri Lanka and Pakistan as well as the ICC Champions Trophy, Graveney was adamant England would not repeat past mistakes and rush injured players back into action before they were fully fit.
England's woeful tour of Australia 2002-03, where the Ashes series was lost 4-1, was wrecked almost before it had begun after desperate gambles on the fitness of Flintoff and Darren Gough, both just returning from injury, backfired with both men playing no part in the Test campaign.
"If you look back to the last time we went to Australia we were trying to force the issue," Graveney admitted. "This time our objective is to deliver our best team as fit as possible for next (northern) winter."
In the meantime Graveney said he would try to boost the confidence of Giles, who has given several pessimistic interviews about his cricket future.
"I've read the same reports about him as everybody else and there is a fine line between being realistic and pessimistic," Graveney said.
"Ashley has had this condition for a period of time and it's obviously a worry for him - if you have an operation to resolve your problem and regrettably you break down again then that's a worry for anyone.
"My job is to underline to Ashley how important he has been and will continue to be for English cricket and give us as much support as we can."