The Gunners have already lost five of their six away games in the Premier League this season, including losses to Liverpool and Manchester City.
Arsenal have a 100 per cent record at the Emirates Stadium this term but their away form has undermined their title challenge.
Tottenham lost 2-0 to Arsenal in the north London derby to fall off the pace in the title race and leave Spurs facing a battle for a top-four place.
Spurs have only managed to collect one point from their last three Premier League games following defeats by Arsenal and Leicester City.
Liverpool and Chelsea have been on impressive unbeaten runs in the Premier League and have a kind run of fixtures until the end of December.
Former Reds captain Thompson is confident that Arsenal and Tottenham will miss out at the expense of Chelsea and Liverpool.
“I’m going for Arsenal and Tottenham to miss out as you don’t really know what you’re going to get from them,” Thompson told Sky Sports.
“Arsene Wenger’s side were very fortunate to get a win at the weekend, while Spurs are struggling to consistently deliver.
“Arsenal are in a transitional period and if Alexis Sanchez and Mesut Ozil do go in January then it will be tough for them to get sufficient quality in, while Spurs also tend to falter against the top sides, particularly away.”
Arsenal finished in fifth place in the Premier League table last season to miss out on a place in the Champions League.
Liverpool managed to beat Arsenal to fourth place, while Spurs finished as runners-up behind eventual champions Chelsea.
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