The FA Cup third-round tie between Wolves and Liverpool will be shown live on BBC One on Monday, 7 January.
The channel will also show Leicester’s game at the winners of the second-round replay between Wrexham and Newport, on Sunday, 6 January.
Wrexham are one of a potential total of five non-League sides in round three.
Elsewhere, non-league Solihull Moors will take on 13-times winners Arsenal if they win their second-round replay against League One side Blackpool, while National League North side Southport will play Tottenham if they can overcome League Two Tranmere.
Both of those ties will be broadcast by BT Sport.