Passive Rules:
A passive check is a special kind of ability check that doesn’t involve any die rolls. Such a check can represent the average result for a task done repeatedly, such as searching for secret doors over and over again, or can be used when the DM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster.
Advantage/Disadvantage:
Sometimes a special ability or spell tells you that you have advantage or disadvantage on an ability check, a saving throw, or an attack roll
Since Advantage/Disadvantage only affect dice rolls, and since there are no dice rolls with passive checks, then advantage in this case wouldn't make a difference.
However, if the wolf starts to actively try to track down something, it would get the advantage.
So, RAW doesn't give you the solution you are looking for - unless you say the wolf has been actively sniffing things out as the group moves, in which case it would have a better chance.