The 26-year-old was tipped to join Tottenham Hotspur in the summer after an impressive second half to the last campaign, in which he scored 14 goals from New Year's Eve onwards.
Despite seeing a proposed move fall flat, Lagerback is confident that King could still find himself at one of the elite top-flight sides if he can recapture the form of 2016-17 for club side Bournemouth.
"Yes, I think he has a fair chance to play in a top-six club," he told reporters. "He has really good qualities, he's physically strong, he's very quick, both with and without the ball, and his finishing technique is really good."
King will sit out Norway's meeting with Northern Ireland on Sunday evening due to a hamstring injury picked up against San Marino last time out.