The Scottish Sun says Bursaspor are ready to blow the rest of the bidders out the water with a staggering £50,000-a-week deal over two-and-a-half years.
Miller has been included in the squad to face Hamilton today.
Boss Ertugrul Saglam said last night: "We know all about the quality of a player like Kenny Miller. It's that type of player we are looking to sign.
"We need someone like him who not only scores goals, but contributes to the team as well.
"We want to get the transfer sorted out as quickly as possible."