According to this Politico article, Senator Rand Paul is about to introduce a bill to permit ex-felons who had been convicted of non-violent crimes to register to vote in all states. However, the bill will only apply to federal elections, because the U.S. Constitution says states can set voting qualifications for state and local elections.
There have been similar bills in many sessions of Congress in the past, but they never pass. This bill might have a better chance than any previous bill, because it has the potential to gain support from Republican members of Congress as well as Democratic members. Thanks to AroundtheCapitol for the link.