The 26-year-old has less than nine months remaining on his contract at Ewood Park and is set to leave the club for free next summer.
According to TEAMtalk, Rangers are confident that they can fend off competition from elsewhere to land Rothwell on a free transfer in July 2022.
However, the midfielder seemingly has his heart set on a move to Ibrox to work under Liverpool and England legend Steven Gerrard.
One previous report has suggested that the Gers may consider recruiting Rothwell in January, with Blackburn looking to cash in on the Englishman if he fails to sign a contract extension.
Rothwell has made 132 appearances across all competitions for Blackburn, scoring nine goals and providing 12 assists. body check tags ::