The bill could come to the Senate floor next week.
"This is the right thing to do. We've needed to do it a long time," Sheran said.
The bill's House companion comes before the judiciary committee Friday morning.
Though there's been bipartisan support in the Senate, Sheran said there are House Republicans who may object to what they may see as a loosening of controls on sex offenders. If someone who leaves the Minnesota Sex Offender Program eventually reoffends, a lawmaker may tout their vote against these reforms.