Norwich sacked Alex Neil at the start of this month and could reportedly turn to Rovers boss Clarke, who was linked with one of their Championship rivals last summer.
Bristol Rovers boss Darrell Clarke
Neil was sacked by the Canaries earlier this month, with former Premier League managers Alan Pardew, Roy Hodgson and Nigel Pearson among the early contenders to replace the Scot.
The Championship side are seemingly no closer to making an appointment, however, and could turn to another up-and-coming boss in Clarke, according to the Sun.
The 39-year-old has led Bristol Rovers to promotions in each of his two full seasons in charge, and could still make it a hat-trick this season with the Gas currently eighth in League One.
Clarke, who began his managerial career at Salisbury City, has already caught the eye of higher-division clubs, having been the subject of an approach from Leeds United last summer.
Leeds boss Garry Monk was also linked with the vacant Norwich job
Eighth-placed Norwich still have an outside chance of making this season's play-offs, where they could face Leeds - now managed by Garry Monk.
Would Clarke be a good appointment for Norwich City?