The 23-year-old midfielder has one year left on his contract but has rejected the Royals' offer of a new deal.
Madejski said: "Do we push him out and try and get as much as we possibly can now or wait until the end of the season, when we get nothing?
"If we sell we must pay a big percentage to Arsenal so it is a very difficult balancing trick."
Reading agreed a sell-on clause when they signed Sidwell from the Gunners in 2003.
Madekski added: "Can we afford to let him run out his contract? Well, that's a moot point.
"We don't know how Sidwell is going to get on in the Premiership. Nobody does because he hasn't played in it yet.
"But to all intents and purposes I think he could be a great player in the Premiership so it is a gamble, like so many things in football these days.
"Quite frankly Steve Coppell and everyone else that is involved in the club have their work cut out with these elaborate games, trying to make it all work."
BBC