The Gunners, who played in the Carabao Cup against Liverpool on Thursday, have a depleted squad for a variety of reasons.
Arsenal are not the first side this season to make the request to the Premier League.
Should their request be granted, it will become the 20th time this season an English top-flight game has been called off.
And the duo have both had enough with games being called off. Watch a video of their comments below...
Speaking before the Premier League match between Brighton and Crystal Palace on Friday evening, Neville said on Sky Sports: "I honestly believe that all teams, not just in the Premier League but the EFL now, must be made to play their fixtures," said Neville.
"Folarin Balogun and Ainsley Maitland-Niles have gone on loan, Granit Xhaka's got a red card - that's not the fault of anybody else. We can't be calling fixtures off.
"If it was purely down to Covid in extraordinary circumstances where there was 10 or 15 players out, but we're now talking about teams for the last few weeks where there's no doubt they've been calling games off based upon whether they think they've got the best squad or team to win a game. It's got to stop.
"Manchester United and other teams have got 30 to 40 players in their squad - I'm not having they can't get 13 to 16 players together.
"For me, it [Arsenal's request] should be rejected.
"Without knowing the exact detail, unless there is an absolute load of Covid cases coming today at Arsenal, I feel having played last night at Liverpool, it has to stop now this and we have to make teams play."
Carragher added: "No other league in Europe is doing this, certainly not in those big leagues. Bayern Munich played a 16-year-old in their last game and that tells you exactly where they are. Why can't we do that? Why can't the young players be given an opportunity in these circumstances?
10-man Arsenal HOLD OFF Liverpool in Carabao Cup semi-final! Full reaction on The Football Terrace...
"Everyone's in the same boat and I'm exactly with Gary. If it's an outbreak of Covid and it's decimated the squad I can understand that, but players being in the AFCON tournament and just normal injuries, that's got nothing to do with it.
"You've got U23 squads and younger players, and this is an opportunity where they can get a chance.
"I know there's a lot riding on Premier League games but at this moment there's no doubt teams up and down this country are taking advantage of the situation."
The Premier League will decide on Saturday morning whether the north London derby goes ahead or not.