The North London rivals are both competing for places in the top four, but now look set to go head-to-head over the signature of striker Kennedy.
Kennedy, 18, can play in midfield or up front, and has burst on to the scene with Stevenage in League Two this season, scoring three goals in his ten games for the club so far.
The Northern Irish youngster is predicted to have a big future, and the Daily Mirror believe that Arsenal and Tottenham have now joined Manchester City in the race for his signature.
They suggest that Arsenal scout Brian McDermott, formerly manager of Leeds United, has been watching Kennedy of late ahead of a possible summer move.
The Gunners have a long history of developing young players under Arsene Wenger, but Tottenham are taking a similar approach with Mauricio Pochettino at the helm.
The Argentine has already handed key first-team roles to Nabil Bentaleb, Ryan Mason and Harry Kane, whilst fellow youngsters DeAndre Yedlin and Dele Alli are projected to feature next season.
The proximity to Stevenage could help Arsenal and Spurs in the race for his signature, though it would be foolish to discount Manchester City, who need to start developing their own young players.