The Gunners turned to the Spanish head coach after Arsene Wenger stood down as Arsenal boss following 22 seasons in charge of the north London outfit.
Arsenal finished in sixth place and outside the top four in successive seasons to fall further behind their traditional rivals.
Emery signed veteran Switzerland defender Stephan Lichtsteiner in a free transfer from Serie A champions Juventus last week.
The Gunners have also been linked with a number of defenders and midfielders as Emery looks to improve the spine of his team.
Arsenal legend Seaman believes the Gunners need to sign three players in the 2018 summer transfer window.
“You’ve got to progress on the season before and we were out of the top four and we were getting left behind by quite a few of the big clubs,” Seaman told Omnisport.
“We need to regroup, have a little restructure of the team and then push on, get into the Champions League again and try and improve on that each season.
“It’s not going to be easy because the big guns are quite a way ahead at the moment. We need steel in the team.
“We need a couple of defenders, dominant defenders, and a dominant midfield player.
“I think the forward side of it, you can leave that alone because we’ve got a lot of firepower there. I’m just a little bit worried about the defence and the art of defending.”
Arsenal finished in sixth spot in the Premier League table to miss out on Champions League for the second successive season.
The Gunners lost 3-0 to Premier League champions Manchester City in the League Cup final at Wembley back in February.
Arsenal reached the Europa League semi-finals for the first time but lost 2-1 to Atletico Madrid in the last four.
The north London side haven’t won the Premier League title in 2003-04 season.
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