The newspaper said Lawrence Tynes has hired lawyer Robert Ortiz, the finance chairman for the New Jersey Republican State Committee, to handle the pardon effort.
In January 2004, Mark Tynes, 31, was found guilty on two counts of marijuana distribution.
He has run out of appeals to reduce his sentence and is not scheduled to be released from a federal prison in Arkansas until 2026.
""Because Lawrence is high-profile, this will get people to look at the story and take a look at what happened to Mark," Ortiz said.
Lawrence said his brother deserves to be in prison, but he feels the sentence is too long.
Tynes' 47-yard field goal in overtime of the NFC championship game beat Green Bay, and New York topped the Patriots 17-14 in Super Bowl XLII, ruining New England's shot at a perfect 19-0 season.
2014: The Year in Music [PHOTOS]