Norwich sacked manager Alex Neil on March 10 after just over two years in charge of the club and assistant Alan Irvine has been placed in temporary charge since.
The former West Bromwich Albion boss has recorded a draw and a win from his two games at the helm and there are suggestions he could be given the job until the end of the season.
However, the Glaswegian has already stated he doesn't want the job on a full-time basis whilst he also expects an appointment to be made before the clash at Aston Villa on April 1.
Several names have been linked with the job, including both Alan Pardew and Roy Hodgson, but it is Giggs who is said to be leading the race.
The Welshman has been out of work since leaving Manchester United last summer but he could be given the opportunity to help the Canaries make a late push for a play-off position.