The trio have taken voluntary redundancy ahead of a divisive channel merger between BBC News Channel and BBC World News.
Deadline is reporting Eades presented his final show for the corporation last week. Gosling is expected to depart at the end of the month, while the timeline for Willcox’s exit is less clear.
The three presenters are against taking part in the recruitment process for a new team of six lead presenters on the new channel.
Around 15 presenters are interviewing for six positions, with all being asked to do screen tests in a small studio.
The BBC is planning to launch the merged channel in April and considers it a central part of plans to cut costs.