Adams took over as Portsmouth manager when Harry Redknapp left for Tottenham.
Bergkamp is currently youth team coach at his former club Ajax.
Adams told the Portsmouth News: “I want my staff sorted sooner rather than later, really by the weekend.
“I’m meeting with a few people and having conversations with a couple of old friends.
“I’ve had a positive meeting with Martin (Keown). Then there’s Dennis (Bergkamp), who is taking the youth team at Ajax and is a good, good man.
“I’ve not spoken to him, but there are a few people I still need to talk to.
“It’s an important part. I’ve got some good people still at the club, which is great, but I need my people in and the sooner I can do that the better.
“Mind you, you don’t have to be an old Arsenal player.”