The 25-year-old midfielder is the club's longest serving player and his current deal runs out next month.
Rovers chairman John Ryan told BBC Radio Sheffield that Green is considering an offer to stay at the Keepmoat Stadium.
"We made a very substantial offer to Paul Green and we sincerely hope he will accept it," said Ryan.
Green is not the only player who the Rovers chairman wants to get under lock and key for next season, with Ryan also desperate to get striker Jason Price to agree new terms.
"Jason is a great player and he'll be staying with us for sure, he is our talisman," said Ryan.
"When he's playing we're playing. We love him in the boardroom, the supporters love him and I hope he will stay for a quite a few years yet."
Price says would like to stay with the newly promoted side: "My contract is up but obviously Doncaster is the place for me at the moment."