Ms Forbes told The Herald she feels this is “probably the one opportunity” for her to secure the role, although she vowed to continue to support the party whatever the outcome.
The Scottish Finance Secretary is facing Health Secretary Humza Yousaf and former community safety minister Ash Regan in the contest to become Scotland’s next first minister, with the result due to be announced on March 27.
Ms Forbes said there has been “turmoil” in the party over the last few days and change is needed.
Her comments come a few days after the resignation of SNP chief executive Peter Murrell, who quit with immediate effect on Saturday following a row over the party’s membership numbers.
His departure came shortly after that of SNP media chief Murray Foote, who said there had been a “serious impediment” to his role.
Ms Forbes told The Herald: “I think it would be unlikely that I would come back in the future. I will continue to support the party and I’ll support the leader, but I feel like I’ve made my campaign clear.
“People know who they’re voting for. It’s up to members to determine which of us is first minister, but I think it’s unlikely that I would stand again. You can never say never, but I think it’s highly, highly unlikely.”
“We need change in this election, and if we don’t get change, then I think it’s going to be really challenging for the party in the future.
“I’ll continue to support the party, but I think it unlikely that I would stand again.”
Ms Forbes, who is a member of the Free Church of Scotland, also said she would work on Sundays as “being first minister is 24/7”.
The MSP, who is currently on maternity leave from her ministerial role, said she will be content whatever the outcome of the contest, as either she will go back to being a new mother or she will be first minister.
She said she will abide by the outcome of the contest whatever it is.