Damon Buffini, managing partner of Permira, wrote to Paul Kenny, general secretary of the GMB, last week to suggest they meet to discuss the private equity firm's work in detail.
"I understand that some apprehension exists regarding the way companies such as Permira operate, and I am eager to set the record straight," Buffini wrote.
A GMB spokesman confirmed that the union had now accepted the invitation and the meeting would take place within the next month.
The spokesman said that the GMB welcomed the opportunity to meet Buffini, but added that he hoped the offer was not simply a PR stunt.
Animosity between the two organisations came to a head last month when the union picketed the foundation's launch dinner.