The 32 year old was at the club's home game against Hull City on Tuesday.
Rovers boss Dean Saunders told BBC Radio Sheffield: "He's just different class, I'll be trying my best [to sign him] and we will see what happens."
But Rovers Chairman John Ryan believes they have missed out on striker El Hadji Diouf. He said: "I've heard he's going to Russia for a king's ransom."
The Senegal international striker, who is a free agent after his contract at Blackburn was cancelled earlier this month, was also present at Doncaster's 1-1 draw with Hull City on Tuesday and met Saunders about a move to the Keepmoat.
Ryan told BBC Radio Sheffield: "I'm not so sure that's going to happen but it was a close-run thing."