The group acquired a 4.61% stake in Norwegian in April with a view to discussions over a full takeover.
Norwegian rebuffed two bids from IAG in May saying they undervalued the business and its prospects.
Other potential suitors included Lufthansa, although Ryanair boss Michael O’Leary denied he made an approach for Norwegian.
IAG boss Willie Walsh said has since confirmed it would now dispose of its stake after failing to negotiate a deal.
“We’re not going to keep the shares, we’re not an investor,” said Walsh upon release of the group’s half year results.
“We bought that small stake to initiate a conversation and if that conversation is not going anywhere, as it’s not, we’re not going to hold on to those shares.”
A Norwegian spokesperson said the airline had nothing further to add on the IAG negotiations.
