Greene King does not intend to put the site on the wider market and hopes it will be possible to sell to the current leaseholders.
The pub has played a big part in the cultural history of the area, with music acts like Amy Winehouse and Arctic Monkeys performing there.
Licensee Ruth Mottram said the team has spent the past five months raising as much money as they could.
She explained: “We managed to secure a commercial mortgage and various other personal loans but we got to stage where we were almost there but not quite there.
“We are lucky that we have a really amazing community at the Hawley. We have been there for 14 years, we have developed a good reputation in that time.”
A tier of rewards has been offered to people who pledge to support the fundraiser, including tote bags, T-shirts, and tankards.
Everyone who makes a pledge will be entered into a draw to win a set-list signed by Amy Winehouse and her band from a gig in Southampton.
Although the campaign launched just a fortnight ago, the pub has been overwhelmed with support from all over the world.
Mottram added: “We have had lots of really lovely messages and support of people behind us.
“Someone who is now in LA but used to live in London was like ‘this is my favourite pub and I really want it to stay open’.
“We have had someone from Brazil and people all around Europe. It is amazing actually.
“Then closer to home, there are people who say ‘this is our regular, we don't want to lose it’.
“There was someone who said she had her 21st [birthday] there 10 years ago and still loved it.
“For us, that pub has always been a place for everyone to come and have a good time. That is what we were always about so it is lovely that people still feel that way. It has been really nice.”
The crowdfunder is one avenue alongside other loans.
Mottram said: “It is quite scary but for us it is about the risk to the business if we don't get [crowdfunding]. That is the impetus of it.”
A spokesperson for Greene King said: “The Hawley Arms is an iconic part of Camden and our first choice throughout has been to sell the pub to the current tenants, who have leased it from us since 2004 and have been largely responsible for its popularity over the past 15 years.
“When we discussed this with them last September they were extremely keen to buy the pub from us and we understand this recent fundraising campaign is to raise the remaining funds to match an independent valuation of the pub.
"We hope our tenants’ campaign is successful and we are continuing to speak with them about the purchase of the Hawley Arms.”
John Cryne, chairman of the North London Campaign for Real Ale (CAMRA) branch, said the group supported the bid.
He added: "It is disappointing that Greene King have, in recent years, disposed of much of their tied estate in North London which creates uncertainty and concern amongst local people who are the lifeblood of those pubs.
"Community owned pubs have been one of the undoubted success stories in the licensed trade, for example The Antwerp Arms in Tottenham, so let us hope there are enough deep pockets amongst supporters to raise what, I imagine, will be a high price to buy the Hawley."