City beat Chelsea 2-0 last time out to maintain their second spot while Spurs' win over West Ham on Monday took them above Chelsea in third place, five points behind City.
Arsenal manager Arsene Wenger said finishing second is possible despite being 11 points behind City in fifth place.
The top three sides win automatic qualification for next season's UEFA Champions League group stage, while the team in fourth place must go through the qualification round.
Since wenger took over in 1996, Arsenal have consistently finished in the top-four, but the last time they ended the season in the top two was in the 2004-05 season.
The last time Spurs finished in the top three was in the 1989-90 season and it has been 50 years since they finished second in the top-flight.
The two North London clubs square up at White Hart Lane this weekend with Spurs having the upperhand over their rival neighbours.
These four clubs battling for the runners-up spot will face each other with 11 remaining game weeks.
City have to visit White Hart Lane, while Spurs themselves have to face Chelsea at Stamford Bridge. Arsenal and Chelsea must all play Manchester United, while Spurs and Chelsea have to visit Anfield.
Everton will have an eye on the Champions League spot but have to face all the top four clubs in the remainder of the season including a trip to Anfield.