The 27-year-old enjoyed an impressive season in the Championship for Tony Mowbray's side, as the Lancashire club looked set to earn a playoff place in the second tier.
However, a poor finish to the campaign saw Blackburn slip away and eventually finish in eighth place, leaving several players set to leave Ewood Park upon the expiration of their contracts in June after refusing to sign new deals.
One of those players is Rothwell, and The Herald is reporting that Norwich hold an interest in bringing the central midfielder to Carrow Road next season, as they look for an immediate return to the top flight following their relegation from the Premier League in the 2021-22 campaign.
Although, Dean Smith's side will face competition for Rothwell's signature from Europa League finalists Rangers, as well as newly-promoted Premier League sides Fulham and Bournemouth, according to the report.
Steven Gerrard was said to be interested in taking Rothwell to Ibrox last summer, whilst Scott Parker's Bournemouth had several bids turned down for him in the January transfer window.
After coming through the Manchester United academy, Rothwell was sent out on loan to Blackpool and Barnsley, before moving on a free transfer to Oxford United in 2016.
The midfielder's performances in League One saw Blackburn swoop in to bring him to Ewood Park, where he has gone on to make 161 appearances for the club across all competitions, scoring 11 goals and registering 18 assists.