"They would like the support of the LDS Church, which I think is important myself," Shurtleff told The Salt Lake Tribune.
"I've had the opportunity over the years to get to know some of the general authorities. I plan to talk to them about this and ask them to get behind it."
The LDS Church supported the Utah Compact, a 2010 document calling for a federal solution to the issue of immigration and compassion for the 11 million undocumented immigrants.
At the time the faith issued a statement saying: "Public officials should create and administer laws that reflect the best of our aspirations as a just and caring society. Such laws will properly balance love for neighbors, family cohesion, and the observance of just and enforceable laws."
Shurtleff, a major player in the Utah Compact, has been the highest-profile Utah politician who supports broad immigration reform that allows illegal immigrants a pathway to citizenship.
He will also try to drum up support among attorneys general, though his successor AG John Swallow has made it clear that he has no interest in being outspoken on this issue.
And Shurtleff has an uphill battle in convincing Utah's members of Congress, who have supported smaller immigration bills but none of whom have supported a process that would give legal status to the undocumented.