The 26-year-old's future has been the subject of much speculation in recent weeks, and it appears that he will be leaving the Scottish giants in the closing stages of the summer transfer window.
According to Football Insider, Blackburn are in advanced talks over a move for Cantwell, and the Championship outfit are confident that a deal will be agreed before Friday's deadline.
Cantwell has asked to leave Rangers this summer and was not included in their preparations for the new season, while he has also not featured in the early stages of the 2024-25 campaign.
The midfielder represented Norwich City ahead of his switch to Scotland, and he has played 86 times in the Championship during his professional career, scoring seven goals and registering nine assists in the process.
Celtic 'make improved offer' for Trusty
Elsewhere, Celtic have reportedly made an improved bid for Sheffield United's Auston Trusty, as the Scottish giants look to secure his signature before the transfer deadline.
Celtic are believed to have had a recent £5m bid for Trusty rejected, but according to Football Insider, they have returned with a fresh offer for the 26-year-old.
Trusty, who is a two-time United States international, arrived at Sheffield United from Arsenal in 2023, and he made 34 appearances during the team's 2023-24 Premier League campaign.
The defender, who has another three years left to run on his contract with the Blades, has scored once in three appearances for his current side during the 2024-25 campaign.
Trusty played for 28 minutes of Sheffield United's EFL Cup second-round fixture with Barnsley on Tuesday night, and that clash could prove to have been his final outing for the club.
Rushworth 'set to join Hull on loan'
Meanwhile, Hull City are allegedly closing in on a loan deal for Brighton & Hove Albion goalkeeper Carl Rushworth.
The 23-year-old has been with Brighton since 2019, but he is yet to make a single first-team appearance for the Seagulls, spending the majority of his career out on loan.
The goalkeeper has represented Worthing, Walsall, Lincoln City and Swansea City during loan spells, making 46 Championship appearances for the latter during the 2023-24 campaign.
According to Football Insider, Rushworth is now preparing to return to the Championship, with Hull set to confirm his signature on loan for the 2024-25 campaign.
The Englishman, who kept 10 clean sheets in England's second tier last season, signed a contract extension with Brighton in July 2023, with his deal at the Amex due to run until June 2027.