The proposal for drinks was suggested after Obama jumped into the race debate last week and pronounced that the Cambridge Police Department acted "stupidly" in arresting Gates, causing a storm of furor from police organizations.
Obama later clarified his remarks, saying that cooler heads should have prevailed on both sides and turned it into what he called a "teachable moment" for the country.
But the White House's beer diplomacy may be a challenging task, as the two men are standing steadfastly by their argument that the other is not telling the truth.
Gates suggested to the New York Times' Maureen Dowd that he expects an apology from Crowley in their meeting with the president.
"It's clearly not going to be like Judge Joe Brown, OK? 'You tell your side, you tell your side.' We have to agree to disagree. But I would be surprised if somebody didn't say, 'I'm sorry you were arrested,'" Gates told Dowd.
Gates denied he told Crowley, as the police report states, that "I'll speak with your mama outside."
Gates added that Crowley must have gotten that line from watching the '70s TV show "Good Times."
"Does it sound logical that I would talk about the mother of a big white guy with a gun?" he asked Dowd. "I'm 5 feet 7 inches and 150 pounds. I don't walk on ice, much less... with some cop in my kitchen. I don't want another hip replacement."
For his part, the sergeant sticks by his claim that he was just doing his job and that Gates was being "provocative."
"I was radioing in his name to our dispatcher so they could record it," Crowley told Boston's WHDH television station. "As I did that, he was continuing his rant about that I was doing this because he was a black man in America, that I was a racist, and to the point that as I was reading his name off my identification card, I couldn't hear myself say it; he was yelling that loud."
Obama initially sided with Gates, telling ABC News that it doesn't make sense to him that the situation escalated to the point that Gates was arrested. He said later it was likely that both men overreacted, but stuck by his claim that Gates should not have been arrested.
The White House is now hoping that it can steer the conversation to be more about racial profiling and race relations than what somebody said.
"I think the president sees this as an opportunity to get dialogue going on an issue that has... been historically troubling and one he has worked on," White House Senior Adviser David Axelrod said Sunday on CBS's "Face the Nation."
Aiming to put a positive spin on the conversation the president on Friday admitted he helped ratchet up, the White House is now hoping to turn the debate into a dialogue.
"There's a real... discussion to be had about how we improve police-community relations and what he [Obama] was concerned about was that his poor choice of words helped pushed the debate in the wrong direction, and he wanted to get it back on track," Axelrod said on CNN's "State of the Union."
As for what beer they'll drink, White House Press Secretary Robert Gibbs noted today that the president hoisted a Budweiser at the All-Star Game in St. Louis earlier this month, while Sgt. Crowley told the president he was more partial to Blue Moon. Gates told the Boston Globe he likes Red Stripe and Beck's, but the White House doesn't stock foreign beer.
And what's the president's personal experience with racial profiling?