Phelps eclipsed the previous record of Soviet gymnast Larisa Latynina's 18 medals, when the U.S. won gold in the 4x200 metres freestyle relay at the aquatic centre on Tuesday night.
Coe, a former Olympic champion himself, said: "I think you can say it is self-evident that he is the most successful. I am not sure he is the greatest.
"It is a pretty good haul, but who is the greatest? In my opinion he is probably not."