(CNN) — House Speaker John Boehner scheduled an election for Republicans to pick his successor on October 28, according to several GOP lawmakers who attended a Wednesday morning party meeting.

The decision to set an election date signals that Boehner is confident that Wisconsin Rep. Paul Ryan will agree to run for speaker.

Ryan, currently the House Ways and Means Committee chairman, said Tuesday that he was open to running, but only if certain conditions were met. He’s seeking the full support of the GOP conference, including important factions of conservatives.

The-CNN-Wire ™ & © 2015 Cable News Network, Inc., a Time Warner Company. All rights reserved. (PHOTO: CNN)