Bassong struggled with a knee injury for much of last season, while fellow defender Turner missed the final few weeks with a groin problem.
Norwich have allowed the duo to continue their rehabilitation at the club, but the rest of the squad will fly to America, with summer signings Ricky van Wolfswinkel, Nathan Redmond, Martin Olsson and Leroy Fer all on board.
Assistant manager Colin Calderwood believes the decision to leave behind Bassong and Turner will speed up their recovery.
"I think it was better for the ones left at home, Seb and Michael especially, to stay there," he said. "They wouldn't have taken part in any of the games over the 10-12 days.
"You can't go straight into the work at too high an intensity. The first thing that we have got to do is make sure that we have got as many players training for 100 per cent of the sessions that we have got - so that they don't miss a session."
Manager Chris Hughton will link-up with the 25-man squad after finalising pre-season plans, which are believed to include a move for Celtic's striker Gary Hooper.
Hughton has been busy in the transfer market since the start of the summer, but admits that some deals might not be completed until the end of the month.
"There are always players you can bring in for lesser money but it is getting harder because every club knows the value of the player they are selling," he said.
"Certainly it is more expensive to buy here in England, but you are finding the foreign clubs know the value of players and so look at bigger fees.
"I would like to get everything done early, but business tends to be done later because of the transfer deadline."