The 27-year-old, who has scored 39 goals in 118 appearances for his country, will join Sean O'Driscoll's squad over the weekend before beginning training with the team on Monday.
He said: "It's a great honour to be trialling at Nottingham Forest. The club's reputation for attractive football is well known in the Middle East and it's exciting to be coming here when a new manager is looking to play the kind of football I want to be part of."
Al-Mutawa, twice nominated for Asia Player of the Year, plays for Kuwait's top club Qadsia SC and has been linked with a move to Malaga in La Liga having also gone out on loan last season.
"I realise the Championship has a tough standard of play but I'm confident my goalscoring and team-working skills will transfer and I can play a major part in Mr O'Driscoll's plans going forwards," he added.