The Premier League outfit are favourites to win the trophy ahead of their semi-final against Wigan on Saturday.
A victory would see them face either Hull or Sheffield United in the decider as they chase their first trophy since 2005.
Seaman, a four-time FA Cup winner, would love to see the trophy drought ended, even if it means missing out on fourth place in the league to Everton - who sit a point behind Arsenal with a game in hand.
"I would take winning the FA Cup over finishing top four," Seaman said.
"Arsenal have been in the Champions League since it began. That has - apparently - become nothing. It's a great achievement, but we want to win something and the FA Cup would be great.
"For Arsenal to win a trophy has been massive for the past eight years. The pressure has been building and everyone has been on the bandwagon of 'You've not won anything.'
"I'm just so desperate for them to win the FA Cup. Win the FA Cup and finish top four then I think everyone will be happy at Arsenal."
Wigan, who are fighting for promotion back to the Premier League, claimed the FA Cup last season after a shock win over Manchester City in the final.
Seaman warned Arsenal against complacency, but said Arsene Wenger's men are capable of beating anyone when at their best.
"I know people are saying they are hot favourites but Wigan are cup holders and they know what it means, what it takes and last season they were surprise winners, beating Man City in the final," he said.
"Arsenal will have to remember that and approach it with caution. But if Arsenal play their game, they beat anybody."
