The London Evening Standard says the two North London clubs both made deadline day enquiries for the out of favour striker - but were rebuffed by the Blues who would prefer him to move to clubs not deemed to be rivals.
The Gunners were looking to secure the services of Demba Ba for the forthcoming campaign and the deal looked likely to happen as the clock ticked down on the deadline.
But Chelsea pulled out of the deal insisting they will not allow one of their prize assets move to another club vying for a top four sport in the Premier League.
Tottenham were also interested in the Senegal international but speculation cooled surrounding a move to White Hart Lane and Chelsea's stance would suggest that Spurs are unlikely to persuade the Blues to allow the 28-year-old a move to north London.
For the big stories and the banter follow us on Twitter: @tribalfootball