"Dembele does not have a chance, not for this game. There is a 50 percent chance he will be back for the Lazio game [in the Europa League]," Spurs manager Andre Villas-Boas told reporters at the club's training ground in Enfield, North London, on Thursday.
Belgian Dembele, who joined Spurs from Fulham in August and made an immediate positive impact on the team, has missed the club's last eight games because of the problem.
Right-back Kyle Walker, striker Jermain Defoe and winger Aaron Lennon all picked up hamstring injuries in last weekend's 2-1 defeat at Manchester City although Spurs hope they will be available for the short trip to Emirates Stadium.
However he said the Gunners' record of Champions League qualification and three Premier League titles still gives them the edge when the clubs' recent history is compared, although Arsenal have won only four of the last 11 League meetings between them.
"I think we are certainly getting nearer in terms of what we are doing for the club," said the manager.
"This is a game in which the passion is extremely high, it's a game that represents three points in the league but represents more than that in the history of North London derbies."
That cost Spurs a place in this season's Champions League when Chelsea won the final. Although they finished sixth, Chelsea took the fourth England spot, bumping Spurs into the Europa League.
When asked if that was a realistic target, Villas-Boas said: "We have to. By what I see in the Premiership, it's obvious that Man United, Man City and Chelsea are running towards the title.
"We are looking at trying to shorten the gap and not letting it grow."
