"If you don’t get invited to this meeting and want to know what it was like, just drink a bottle of gin and then waterboard yourself," Costolo tweeted Friday.
The former Twitter chief, who ran the company from 2010 to 2015, was referencing news of Trump's impending meeting with entrepreneurs and venture capitalists in the tech space later this month, according to BuzzFeed.
Silicon Valley leaders have had a complicated relationship with the President since he was elected in November. A number of powerful industry leaders, including Apple's Tim Cook, Facebook's Sheryl Sandberg and Tesla's Elon Musk, met with Trump in December to smooth tensions following disagreements throughout his campaign.
Musk and Uber CEO Travis Kalanick also participated in White House advisory councils. The latter came under fire amid company scandals to the point of his resignation due to pressure from Uber employees and outside groups.
The Tesla chief meanwhile opted to stay on until Trump vowed to withdraw the U.S. from the Paris climate agreement at the beginning of June.