Port’s home game with Tranmere Rovers was selected and will be on Monday December 17 - broadcast on BT Sport.
That tie was interesting enough already before the draw for the third round was made.
The winner of the game will welcome Premier League powerhouses Tottenham Hotspur in January.
Southport earned the chance thanks to a brilliant performance at Prenton Park on Sunday.
Manager Liam Watson said: “I couldn’t be prouder of the players - they were absolutely magnificent.
“We fully deserved it all well and the lads should rightly be thrilled by what they have done.”
Solihull will face Arsenal but they must get past Blackpool at Bloomfield Road first following a 0-0 draw on Friday night.
That game will also be live on BT Sport on Tuesday December 18.