Former Leeds forward Bridges is out of contract after being released by Hull while Craig is a 20-year-old who was with Rangers before being allowed to leave.
Canaries boss Bryan Gunn told the club's official website: "Michael Bridges is a very experienced campaigner having played in the Premier League, Championship and League One.
"It's an open-ended arrangement on both sides so we'll see how it goes over the days ahead.
"Chris Craig is a diminutive striker who has high skill levels and hopefully we'll be in a position to make decisions on both of them by the end of the week."
Source: Team_Talk