The list of players up for induction was released Monday.
Gossage, who retired in 1994 with a 124-107 record and 310 saves, was just 21 votes short of the number needed to win a place in the hall last year.
Also on this year's ballot is longtime Boston slugger Jim Rice, who was 63 votes short last year.
A player must be named on 75 percent of the ballots sent to 575 longtime members of the Baseball Writers Association of America to be elected to the Hall of Fame in Cooperstown, N.Y.
This year's list of 25 names, including 11 on the ballot for the first time, is one of the shortest in the history of the process. A player is eligible for inclusion five years after he retires from baseball.
In addition to Gossage and Rice, the players on the 2008 ballot are: Brady Anderson, Harold Baines, Rod Beck, Bert Blyleven, Dave Concepcion, Andre Dawson, Shawon Dunston, Chuck Finley, Travis Fryman, Tommy
Hall of Fame voting results are to be announced Jan. 8.
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'