Border said yesterday that Warne was improving steadily but had yet to find his best form.
"He's probably just a few weeks from bowling somewhere near his best, so that will count him out of the test series," Border said.
"It would have been nice for him to make his big entrance at the MCG for the fairy-tale comeback, but it doesn't look like it's going to happen."
Border said any pressure on Warne to make a hasty return had been lifted after Australia retained the Ashes by winning the third Test in Adelaide. Border also said the selectors were lucky to have such a creditable replacement in the leg-spinner Stuart MacGill.
Surgery on Warne's shoulder has prevented him playing Test cricket since the third match against India in March.
He returned to first-class cricket last month and will play for Victoria against New South Wales in a Sheffield Shield match starting at the Sydney Cricket Ground today.
MacGill, who plays for New South Wales, withdrew from that match yesterday to rest a hamstring injury, but is certain to be ready for the fourth Test.
It had been hoped that Warne would be fit enough to make his Test return in the fourth Test at the MCG, starting on Boxing Day. If he misses that match, he is almost certain to miss the fifth and final Test which begins in Sydney on 2 January.
Thick fog again made play impossible on the second day of the third and final Test between Pakistan and Zimbabwe at Faisalabad yesterday. The tourists lead the series 1-0, having won the first Test in Peshawar.
Play was also abandoned on the first day of the first Test between New Zealand and India at Carisbrook yesterday after bad light and persistent drizzle.Reuse content