Coe, vice-president of the International Association of Athletics Federations, finds out on Wednesday if he will succeed Lamine Diack.
The 58-year-old is running against Ukrainian ex-pole vaulter Sergey Bubka to lead the IAAF, as the sport faces widespread doping claims.
"He can do a great job," Farah said.
"I hope Seb gets the job because he can change athletics."
Former London 2012 chairman Coe has pledged to increase resources in the "battle for the sport's integrity" and has vowed to set up an independent anti-doping agency for athletics.
World 5,000m and 10,000m champion Farah, 32, added: "What Lord Coe did for London 2012 was incredible.
"I don't want to see anything bad in athletics because it's the sport that I do every day and the sport that I love."
Doping allegations were recently made about Farah's coach Alberto Salazar in a BBC Panorama investigation.
Salazar denies the claims and a separate UK Athletics investigation found no reason to question Farah's training regime at the Oregon Project base.
Outgoing IAAF president Diack says he is confident about the future as the sport prepares to elect his replacement.
The 82-year-old Senegalese has run the governing body for 16 years. He told the opening day of the 99th IAAF Council on Monday: "I have laid the foundations for the future of the IAAF with our two great champions.
"Whoever the athletics family elects he will be a bona fide son of our sport. I am all the more confident of what we have in store."
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