The Gunners saw their promising title charge falter in the final months of this season, something which was largely due to increased defensive lapses and primary centre-forward Olivier Giroud going nearly four months without a league goal from mid-January until early May.
Arsene Wenger has looked to address the goalscoring problem by activating Vardy's release clause of around £20 million at Leicester City, and the England striker is currently mulling over a move to the Emirates Stadium.
The 29-year-old scored 24 goals in 36 league matches last season, and Seaman believes he would be a quality addition for his former side.
However, the ex-England number one stressed that Wenger still needs to bring in a new central defender this summer if Arsenal are to finally win another league title next season.
Seaman told the Express: "I was hoping that [Vardy] would come. People say he’s not an Arsenal type of player but he just gives us another option. Of course Jamie Vardy is not just a guy that gets the ball over the top. Come on, he’s got a lot more to his game than that.
"They need a central defender, they’ve signed a new midfield player now, get Vardy and then we’re looking good. You look at the spine of the team. You’ve got Petr Cech in goal, brilliant. We maybe need one centre-half and then a striker.
"But they are additions to a great squad, it’s not as though the squad is crying out for it or performing badly. We did have a good season, we finished second."
While Gunners fans may not agree with Seaman about how much last season can be defined as a success, they will surely approve of his assessment that a new defensive reinforcement is needed.
First though, they are desperate to see another striker added to their side, although it is beginning to seem as though that may not be Vardy, with former Arsenal star Ray Parlour claiming earlier this week that the Foxes man had changed his mind about a move and cut short his medical.