Aston Villa launched a £6m bid for the striker with add-ons taking the overall value to £10m, but Boro are looking for at least £9m upfront for the player.
Middlesbrough have recently added Rudy Gestede and Patrick Bamford to their attacking options and also have former Man City star Alvaro Negredo on loan from Valencia.
This means that Rhodes is likely to be free to leave the Riverside, but chiefs on Teesside want to recoup the £9m they paid for him last January when he joined from Blackburn.
The 26-year-old has started just twice for Boro this season and is being chased by a number of Championship sides due to his record in England's second tier.
Villa are in desperate need for a striker, too. Ivorian Jonathan Kodjia is currently at the African Cup of Nations and Steve Bruce's side recently sold Gestede to Rhodes' current side, Boro. Big-money summer signing Ross McCormack has also struggled, scoring just three goals in 20 appearances, meaning that this will most probably not be Villa's only bid for Rhodes.