Lukaku was part of the pre-season tour of Australia and the Far East, but did not play because of injury.
United remain in talks with Inter Milan over the Belgium international, 26, but there is no agreement over a fee.
The Old Trafford club rejected a 60m euro (£54m) bid for Lukaku from the Italian giants earlier in July.
Inter boss Antonio Conte has said the forward is his number one summer transfer target.
Italy full-back Matteo Darmian, another player linked with move away from United, is also absent from the squad heading to Norway for Tuesday's match.
Ole Gunnar Solskjaer's side play their final pre-season friendly against AC Milan in Cardiff on Saturday (kick-off 17:30 BST). ufabet
Manchester United squad to play Kristiansund: David De Gea, Lee Grant, Joel Pereira, Sergio Romero; Diogo Dalot, Phil Jones, Victor Lindelof, Marcos Rojo, Luke Shaw, Chris Smalling, Axel Tuanzebe, Aaron Wan-Bissaka, Ashley Young; Fred, Angel Gomes, Daniel James, Jesse Lingard, Juan Mata, Nemanja Matic, Scott McTominay, Andreas Pereira, Paul Pogba; Tahith Chong, Mason Greenwood, Anthony Martial, Marcus Rashford.