The highly-rated youngster has a £4.2million buy-out clause written into his contract, and would be a perfect addition to the Gunners' first-team squad, according to the club legend.
Arsene Wenger has so far failed to make much impact during the summer transfer window, adding free agents Yaya Sanogo and Mathieu Flamini, whilst also missing out on a number of high-profile signings.
Having failed with bids for Luis Suarez, Gonzalo Higuain and Wayne Rooney, Adams says that the club are in fact looking at strengthening in the wrong area, and should focus their attention on defensive or midfield reinforcements.
"Arsenal will always score goals," the former defender told talkSPORT's Hawksbee and Jacobs show. "They can score goals from all the pitch. There is no problem going forward.
"They have enough offensive players. They just need someone to lock it up when it breaks down."
He added: "I can understand the frustration of the [Arsenal] fans. They've seen a lot of top players go out of the door in recent years and you can't win anything without the best players, and too many have gone."
England U21 international Dier, although in the early stages of his career, has been tipped for a bright future in the game, and Adams would love to see Arsenal beat rival suitors Chelsea to the talented teenager's signature.
"There's a kid at Sporting Lisbon, Eric Dier, who's English, he's 19, maybe he could fill the gap?" added Adams. "He certainly wouldn't cost £30m or £50m.
"So can Arsene [Wenger] unearth another one? That's what I'd be looking for."
Chelsea manager Jose Mourinho has a reputation for signing more established players for big money transfers, and so it would come as some surprise if Dier ended up at Stamford Bridge this summer, but a switch to the Emirates Stadium is a much more conceivable concept.