The Scotsman’s sister title, the Sheffield Star, claims the Scotland international is a target for the Ibrox club ahead of Steven Gerrard’s first day in charge on Friday.
The 28-year-old striker signed for the Owls for a club record fee of £8 million from Middlesbrough, but has found the net just ten times in 56 matches since moving to Hillsborough.
Rhodes struggled for game time during the last campaign under manager Jos Luhukay, and has been linked with a move away from Yorkshire.
Sunderland were credited with an interest in the former Huddersfield Town hitman earlier this season although the Black Cats’ relegation to League One, and arrival of new manager Jack Ross, suggests any interest may now be over.
Wednesday currently have eight strikers in their first team squad - including Steven Fletcher, Fernando Forestieri, Gary Hooper, Lucas Joao and Atdhe Nuhiu - and with Rangers likely to be one of the few clubs able to pay both a transfer fee and Rhodes’ wages, the out-of-favour attacker could be set for a move north.