Ryan was sentenced following his convictions for racketeering, mail fraud, tax evasion and lying to the FBI. He has since been freed and is serving the rest of his sentence under house arrest.
The justices rejected review of Ryan's case in a one-line order without comment.
The mail-fraud charge alleged Ryan defrauded Illinois of its intangible right to his honest services by covertly acting in the interests of some private supporters, rather than as a "fiduciary" for the state's citizens.
But the Supreme Court ruled in 2010 that the federal law covering "denial of honest services" covers only bribery and kickback schemes.
A federal appeals court twice rejected Ryan's argument that his jury instructions were defective because they permitted jurors to convict him on an honest-services theory without finding a bribe or a kickback.