"Mo is fearless and I would pick him to do it," said Lord Coe. "I always thought his better chance was the five.
"Other countries run as teams and try to determine the tactics and the impact of that is lessened at half-distance."
The 5,000m heats start on Wednesday, with the final on Saturday (19:45 BST).
Farah, 29, won both disciplines at the European Championships in 2010 - retaining his 5,000m crown this year - and came close to a double in the World Championships in South Korea last year, winning silver in the 10,000m before collecting gold in the 5,000m.
Coe won 1500m gold at the Moscow Olympics in 1980 and Los Angeles in 1984 but never managed two golds at one Games, taking silver in the 800m on both occasions.
Dame Kelly Holmes won both middle distance races, the 800m and 1500m, in Athens in 2004 and Coe believes Farah has the psychological strength to match her achievement.
"If you're going for a double, it is mentally tough more than anything else," said Coe.
"Kelly Holmes managed it but most don't - I didn't ever manage to do it."
In addition to European and world titles at 5,000m in the past year, Farah has also set a new British record and a new European indoor record at the distance.
Coe says such achievements are indicators of the Briton's growing maturity and experience.
"In every championship he has got a little bit better," he said.
"[The 10,000m win] was an assured performance. He went just at the right time.
"When he was around 600 metres out, he looked up at the screen and I thought he was just judging and planning when to go, and he timed it perfectly."