19/01/2012 11:33 +0100 – The 23-year-old is travelling to England to undergo a medical and discuss personal terms.
Bordeaux say that subject to Modeste passing his medical and agreeing terms, he will join Rovers on loan until the end of the season, but without an option to make the deal permanent at the end of that period.
The Cannes-born forward has scored three goals for Bordeaux in 15 Ligue 1 appearances. His last goal for Les Girondins was scored in a 2-0 win over Caen in November.
If a deal can be completed, he will be Rovers boss Steve Kean's first significant acquisition of the January transfer window.
Kean admits that Modeste has a lot to prove after the former France Under-21 striker's failure to live up to expectations at Bordeaux.
Modeste could be in the Blackburn squad to face Everton this weekend if he passes a medical and his six-month loan is completed in time.
He moved from Nice to Bordeaux for around £3.5million in 2010, but lost his place in the Ligue 1 side before Christmas.
Modeste had attracted interest from Arsenal when at Nice after scoring six goals in 15 appearances for France Under-21s but his career then failed to take off.
Kean said: "He's got a lot to prove as he went to Bordeaux for a big fee but I think he could be a real addition to our squad.
"He's not too young but he's not in the twilight of his career either, and if you look at his attributes as a player he's got something we don't have.
"He likes to play on the shoulder of the defender, to run in behind, he can stretch the game and technically he's good.
"He would certainly complement the other strikers we have and we hope it will be an exciting loan period initially and that's something we could maybe continue further on."
Meanwhile, Scott Dann is back in the squad to travel to Everton after a groin injury.