Both of the London clubs are looking to break back into the Champions League qualification spots this term after having missed out on a spot in the top four last season.
Arsenal ended up in sixth place in the table under Arsene Wenger, while Chelsea FC finished in fifth spot under Antonio Conte.
Both clubs are well in the mix to secure a top-four finish, and Chelsea FC have a game in hand over their closest rivals as the race for Champions League qualification hots up.
However, former Tottenham Hotspur manager Sherwood feels that both of the London clubs are likely to miss out on Champions League spots in the Premier League this season.
Asked to predict which teams will miss out on top-four finishes this season, Sherwood told BT Sport on Saturday night: “Arsenal and Chelsea.
“I still feel Tottenham will consolidate in the top four. But it’s fine margins and if they don’t it will be a very bad season for Tottenham.
“Manchester United are coming like a train and I think they’ll do very well in the run-in.
“Tottenham will be good enough to hold onto third or fourth.”
Arsenal will return to Europa League action on Thursday night when they host Rennes at The Emirates after the 3-1 loss last week in the first leg.
Meanwhile, Chelsea FC will travel to Ukraine to take on Dynamo Kiev after their 3-0 win at Stamford Bridge last Thursday night.
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