Coventry will apparently pick up a £144,000 cheque from the broadcasters, money that will be welcomed by the club following their relegation from the Championship and the move away from the Ricoh Arena in the summer.
The Sky Blue Trust has reacted with some dismay to the news, claiming the club would have carried several thousand fans to London on a Saturday.
Coventry fans already have to travel 34 miles to watch their side play at Northampton following the club's bitter departure from the Ricoh.
"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," said Jan Mokrzycki, spokesperson for supporters' group Sky Blue Trust.
"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."
Mokrzycki claims a lot of a schoolkids will miss out on attending the match against the Premier League leaders at 7:45 pm on January 24 due to the 200-mile round trip.
The last train out of London heading for Coventry departs Euston at 11:30 pm.
"It's almost going to be straight from school, straight on to a coach, straight down there," he said. "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."
Coventry won the FA Cup in 1987 with a famous 3-2 victory over Tottenham after extra-time in the final.
"I was lucky enough to be there in 1987 so the FA Cup is particularly special to me," said Mokrzycki.
"But the TV companies are ripping it apart and devaluing the competition. Coventry might be getting TV money, but a match on a Friday night will cut the number of fans who travel by half."