By Daniel Strauss - 12/05/12 05:46 PM EST
Gutierrez, an outspoken advocate of immigrant rights, said he is scheduled to meet with Ryan sometime next week.
"We're going to see each other next week; we're talking," Gutierrez said on MSNBC. "He says to me 'Luis, I want to do it because it's the right thing, I don't want to deal with it from a political point of view.' I think that's very, very encouraging."
The Illinois Democrat said he was meeting Wednesday with another Republican, Rep. Raúl Labrador (R-Idaho), to discuss immigration as well.
"Here's what I know, I'm going to be seeing Mr. Labrador this afternoon. Republican from Idaho, sitting down with him," Gutierrez. "He wants to talk."
Labrador was an immigration attorney before serving in Congress.
Republicans have shown an openness to negotiating on immigration reform in the aftermath of November's election, in which the Hispanic vote went overwhelmingly to Democrats.
Earlier Wednesday, Sen. Marco Rubio (R-Fla.), who had been crafting an immigration reform alternative to Democrats' DREAM Act, said that there was more than a 50-50 chance of Congress passing immigration reform in 2013. Rubio is a potential presidential candidate in 2016.