"Attila's mind had been bent on going to Rome. But his followers, as the historian Priscus relates, took him away, not out of regard for the city to which they were hostile, but because they remembered the case of Alaric, the former king of the Visigoths. They distrusted the good fortune of their own king, inasmuch as Alaric did not live long after the sack of Rome, but straightway departed this life. (223) Therefore while Attila's spirit was wavering in doubt between going and not going, and he still lingered to ponder the matter, an embassy came to him from Rome to seek peace. Pope Leo himself came to meet him in the Ambuleian district of the Veneti at the well-travelled ford of the river Mincius. Then Attila quickly put aside his usual fury, turned back on the way he had advanced from beyond the Danube and departed with the promise of peace. But above all he declared and avowed with threats that he would bring worse things upon Italy, unless they sent him Honoria, the sister of the Emperor Valentinian and daughter of Augusta Placidia, with her due share of the royal wealth."
Jordanes The Origins and Deeds of the Goths, translated by Charles C. Mierow
Michael A. Babcock studies this event in his Solving the Murder of Attila the Hun. Babcock does not believe there is evidence that Attila had ever been in Rome before, but he would have been aware there was great wealth to plunder. He also would have known it was virtually undefended, but he walked away, anyway.
Among the most satisfactory of Babcock's suggestions is the idea that Attila, who was superstitious, was afraid that the fate of the Visigothic leader Alaric (the Alaric curse) would be his once he sacked Rome. Shortly after the sack of Rome in 410, Alaric lost his fleet to a storm and before he could make other arrangements, he died suddenly.