He has since confirmed that talks with those governments are "ongoing".
"We have offered all @BrewDog bars to help with a quick roll out of the vaccine. For free," Watt said.
"We have waiting areas, huge refrigerators & ace people who can help organise."
The brewery also has plans to offer anyone vaccinated at a BrewDog pub a "special commemorative beer" and has asked followers to help choose the name of the new brew.
While the negotiations have not led to any decision yet, the brewery's gesture has already inspired others to make similar offers.
Nightingale Club in Birmingham has also put its hand up to offer with vaccine rollout for free.
UK PM Boris Johnson has revealed that one in 50 people in England are infected with Covid-19 as he promises to keep the country updated "jab by jab" on his mission to vaccinate the most vulnerable by mid next month.
Johnson joined UK health bosses for a Downing St briefing to tell the nation their lockdown had been inevitable after a virulent new strain of the virus spread rapidly across the country.
Chief scientific adviser Sir Patrick Vallance warned that the changing nature of the virus meant vaccines will have to be altered.
"The virus probably will mutate. Different vaccines will be needed at that point," he said.
Johnson also refused to confirm that schools would reopen before the summer holidays but insisted that it was a top priority.
England is set to remain in lockdown until at least March, and some measures could stay in place for even longer, as hospitals struggle to cope with the highly contagious new strain of the coronavirus.
Announcing the lockdown on Monday, Prime Minister Boris Johnson said the restrictions were expected to last until the middle of next month, when the UK's National Health Service hoped to have vaccinated priority groups, including older care home residents and staff, over 70s, frontline health workers and the clinically extremely vulnerable.
