Both Arsenal and Manchester United got their Premier League campaigns off to a winning start.
The Gunners won 1-0 at Newcastle United thanks to a second-half goal from Pierre-Emerick Aubameyang.
Meanwhile, United brushed aside Chelsea 4-0 in an impressive display at Old Trafford.
Both Cole and Merson agree their former sides will not be challenging for the title this season.
However, Cole says the Red Devils will make the top four and Arsenal will not, as long as Tottenham do not sell Christian Eriksen.
“It’s crazy how we’re talking about finishing in the top four at the start of seasons,” Cole said on The Debate.
“Man United are going to finish in there.
“If Spurs lose Eriksen, they’ll struggle.”
Merson agreed losing Eriksen would be a big blow to Tottenham’s hopes of qualifying for the Champions League again.
However, he has been impressed by Arsenal’s summer transfer business.
And therefore he reckons Unai Emery’s side will break into the top four at the expense of Manchester United.
“I don’t think Man United [will get in the top four],” Merson said.
“I think Arsenal will pip Man United.
“I think Man City win it, then Liverpool, Tottenham if they keep Eriksen, then I just go Arsenal over Man United and Chelsea.”
Arsenal are next in action on Saturday when they host Burnley (12.30pm).
United are away to Wolves the following Monday (8pm).