The former Germany coach had only been in the job for a short time following Fabio Capello's exit, however the team have struggled at the start of the Serie A season.
Giallorossi's sporting director Franco Baldini confirmed after Roma's stunning defeat to Bologna that Voller was ready to quit his job.
"After the match, Voller wanted to talk with me and he announced his resignation," said Baldini. "I can confirm Voller's plan to resign.
"I've asked him to think about it, but he seemed certain. If there is someone responsible for this situation, surely it isn't Voller.
"He arrived only few weeks ago and hasn't had the time to see all players and to train with them. Players have been selected by the club and by me, so the responsibility isn't Voller's."
Rumours in Italy are already linking former Chievo and Porto coach Gigi Delneri to the post, although Voller is expected to make a firm decision on Sunday morning.
Bologna coach Carlo Mazzone was quick to praise Voller and believes the crisis at the club is not his fault.
"It's a pity, he's a good coach," said Mazzone. "I think that Roma are going through a bad patch.
"They need their most important players right now. I hope Roma can find the right person to bring glory back to the club."
they two teams face each other on tuesday night
