Doncaster manager Dean Saunders has launched the ambitious bid as he overhauls the Rovers team.
The former Welsh international has already signed former Wigan Athletic full back Pascal Chimbonda on a free transfer and he is looking to strengthen the goalkeeping spot with the addition of Kirkland.
Latics boss Roberto Martinez is said to be keen on the move as Kirkland requires first team football to maintain his sharpness.
Lee Nicholls and Mike Pollitt are both present understudies to summer addition Ali Al-Habsi at the DW Stadium.
