The meeting comes amid speculation that Obama, who said on Tuesday that the four-star officer showed "poor judgment”, may sack McChrystal for his disrespect.
In Rolling Stone magazine's profile entitled "The Runaway General", which follws the general on a visit to Paris, McChrystal aides mock Vice-President Joe Biden, call the President's national security adviser "a clown", and say the general was "disappointed" by his first meeting with Obama.
McChrystal himself is quoted deriding the US special envoy to the region, Richard Holbrooke, and saying he felt "betrayed" by the ambassador to Kabul, Karl Eikenberry, who had raised pointed objections to his war strategy.
He is also quoted as saying, "I'd would rather have my ass kicked by a roomful of people" than keep a dinner engagement with an unamed French minister, while an aide describes the prospect as "fucking gay".
The minister has not yet been identified, although Libération newspaper says that Defence Minister Hervé Morin did not meet him while he was in France.
White House spokesman Robert Gibbs said Obama was "angry" when he read the article, and refused to rule out that, as commander-in-chief, the President would fire McChrystal.
"General McChrystal has fought bravely on behalf of this country for a long time. Nobody could or should take that away from him, and nobody will," Gibbs said.
"But there has clearly been an enormous mistake in judgment to which he's going to have to answer to."
Obama said Tuesday he wanted to first talk with McChrystal before making any decision on his fate, but US media reported that the general had already offered his resignation.
McChrystal issued a statement late Monday apologising for his remarks and one of his media officers, Duncan Boothby, a civilian, has already resigned.
The stakes were high for Obama as he faced two unattractive options, firing McChrystal and possibly derailing the war effort, or tolerating the episode and taking the risk of appearing weak.
The article brought to the surface lingering tensions between military leaders and the White House, just as the US deploys 30,000 more troops to the Afghan war, now in its ninth year.
|Click here for France 24's blog by Leela Jacinto - Runaway Lips: The Other Side of McChrystal’s Big ‘Oh Boy’|