Although the fee has not yet been disclosed, the club said it is significantly higher than their current record received transfer fee, the £2.75million they received from Ipswich for Marcus Stewart in 2000.
Rovers boss Steve Kean has expressed his delight as Rhodes edges closer to a move to Ewood Park.
The Scottish international has reportedly agreed a five-year deal bringing an end to a three-year stay in West Yorkshire.
"It's all going well and we're nearly there," Kean told Sky Sports. "It's been really hard to get done but we're nearly there.
"Anybody who has seen Jordan play knows he can score a number of goals. And to be fair, the signings we've already made so far show where we want to go and how we want to play.
"Jordan has seen those players, he's seen what we're trying to do here and he wants to be a part of that."