The FA Cup was halted before the quarter-finals because of the pandemic, but tournament organizers hope to complete it alongside the Premier League.
The four matches in the last eight will be played over the weekend of June 27 and 28, with no decision reached yet on whether these will be played on a home-and-away basis as normal or at neutral venues.
Leicester take on Chelsea, Newcastle face holders Manchester City, Sheffield United play Arsenal and Norwich meet Manchester United.
The semi-finals will be played on July 11 and 12, with the intention being for those matches and the final to be played at Wembley as usual.
All the ties will be behind closed doors.
The news will be a boost to the FA from a financial perspective, with its chief executive Mark Bullingham warning in April of the governing body suffering losses of up to £150 million ($184 million) as a result of the disruption caused by the health crisis.
“The competition has been an integral part of the English football calendar for nearly 150 years, and we’d like to thank the Premier League executive and clubs for their support in scheduling the remaining matches during this unprecedented time,” Bullingham said on Friday.
“This has been a difficult period for many people and while this is a positive step, the restart date is dependent on all safety measures being met. The health and well-being of players, staff and supporters remain our priority.”