Sullivan is one of 10 Doncaster players who have been invited by manager Sean O'Driscoll to agree fresh terms at the Championship club.
O'Driscoll has also told Paul Heffernan, Lewis Guy, Sean McDaid, Charles Fisher, John Spicer and Ben Smith they can move on.
Apart from Sullivan, the other players pondering new contracts are Mark Wilson, Gareth Roberts, Mustapha Dumbuya, James Hayter, Adam Lockwood, John Oster, Robbie Clark, Waide Fairhurst and Gary Woods.
Reserve keeper Smith told BBC Radio Sheffield: "They've offered him [Sullivan] something and I know that he feels he's got another year or two left.
"I've got it in my head that I will be going and it's time for me to move."
Source: BBC Sport