The televised tie at the Emirates Stadium on January 24 will be the opening fourth-round clash, the first of five matches to be screened live across the weekend.
While the B£144,000 broadcast fee will be welcomed by Coventry, especially following the club's relegation to League One and their bitter move away from the Ricoh Arena in the summer, concerns have been raised over how many Sky Blues fans will make the trip to London.
Jan Mokrzycki, spokesperson for supporters' group Sky Blue Trust, said: "The general reaction seems to be that it is not a very good idea because people are going to have to take time off work and some people might not be able to go.
"If it had been a Saturday we could have sold about seven or eight thousand - on a Friday night we will probably take four or five (thousand)."
Mokrzycki believes many school-age supporters may be unable to attend the attractive fixture, which will be shown on BT Sport.
He said: "It's almost going to be straight from school, straight on to a coach, straight down there. It could have been a nice day out - to get down is going to be a rush.
"There will be those who just can't make it because Dad doesn't finish work until five or whatever.
"Basically supporters are the least of the minor considerations - it's money first, money second, money third and oh yeah there's the supporters."
The other matches to be screened are Saturday's lunchtime ITV1 clash which will see Liverpool travel to either Bournemouth or Burton Albion, before Merseyside rivals Everton head to Stevenage at 5:30pm in a game to be shown on BT Sport.
On Sunday, Sheffield United - who knocked out Aston Villa - will host the winners of the replay between Fulham and Norwich on BT Sport, while the live ITV1 tie is the all-Barclays Premier League affair between Chelsea and Stoke at Stamford Bridge, which kicks of at 3:30pm.
- Sports & Recreation