Instead, he awarded the armband to Jones, who he feels will have helpful company once the Lions take to field for the decider in Sydney.
"He leads from the front," Gatland told BBC Sport. "He's been outstanding in the lead-up to games and was one of the first names on the teamsheet when we picked the side for the first two Tests.
"He'll lead by example. There's a little bit of pressure taken off him with the fact that Geoff Parling will be calling the lineout. There are leaders in other positions as well."
The final Test takes place in Sydney on Saturday.