And ex-Gunners captain Vieira, now manager of Nice, could be a candidate.
"I am sure Arsenal fans would love Patrick to come back to the club. Knowing Patrick, I think he would be the right man," Seaman told BBC Radio 5 Live's Football Daily Podcast.
"I knew what he was like as a player. I knew what he was like as a captain. He was a born leader and everybody knows that. Maybe go down that route instead of a tried and tested route."
On caretaker boss Freddie Ljungberg, Seaman was less enthusiastic.
"This job is much bigger than what Freddie is used to at the moment," said the ex-England international.
"He has only just got into the coaching side of the game and he will be really avant-garde as a manager but while he is taking charge now, please try and get some sort of defensive formation sorted out."