Eriksson, 77, resigns from the RF post at the spring National Sports Meeting.
He is proposed by the Swedish Cycling Association for the position in SOK.
Hans von Uthmann and Per Palmström are the other candidates.
von Utmann has sat on the SOK's board for the past twelve years, currently as acting vice-chairman, and was previously chairman of the Swedish Basketball Association.
He is suggested by basketball, skiing, canoeing, tennis and equestrian sports.
Gives its proposal March 30
Palmström previously served twelve years on the SOK's board of which eight years as vice chairman.
He has also been vice chairman of the Swedish Fencing Association and a member of the International Fencing Association's board.
Per is suggested by multi-sport, taekwondo and Swe Sports (skating, tobogganing and roller sports).
On April 20, the SOK will elect a new chairman after Mats Årjes, who resigned earlier this year after he was prosecuted for suspicions of sexual harassment.
He was recently acquitted in the district court.
A further four seats on SOK's board are to be filled at the annual meeting on 20 April.
"The selection committee's work is now entering the next phase with interviews of the nominees and taking references.
After anchoring with the special associations, the election committee will give its proposal on March 30," says election committee chairman Patrik Tengwall in a press release.