Derby County's FA Cup fourth-round home match against Leicester City will be shown live on BBC One, as will the ties between Millwall and Watford and Manchester United and Wigan Athletic.
Premier League champions Leicester will visit Championship side Derby on Friday, 27 January at 19:55 GMT.
League One Millwall host Premier League Watford two days later at 12:00.
That game will be followed at 16:00 by FA Cup holders Manchester United against Championship strugglers Wigan.
The Old Trafford tie was confirmed after Crystal Palace's third-round replay victory over Bolton on 17 January - had Bolton progressed, their match against Manchester City would have been televised.