I completed the companions questline, and I want to do the purity quests for Farkas and Vilkas. I can talk to Vilkas, and he gives me work which leads to his purification quest. However, there is no dialogue for work with Farkas when I talk to him, even though the arrow points towards Farkas when I select the objecive "Talk to the companion's leaders for work". Aela still also gives me quests, however, Farkas doesn't.

Also, I'm on console so this can't be the result of mods.

Has this happened to anyone? And how can this be fixed?

Happened to me. I then helped out Aela with a totem of Hircine, and when I was finished with her, I went to Farkas and the "work" option appeared.

So try doing another job for someone else, then return to Farkas to see if that option appears.

I just took your advice, and did a totem of Hircine quest for Aela. The work option for Farkas still hasn't appeared yet. I'll try doing one with Vilkas and see how it pans out.

I've never received any of the Totems or Purification quests from any of the Companions. I've completed the quest line and cured myself of Lycanthropy and they won't even give me jobs anymore.. They just say I'm already doing something for Vilkas and I'm not.. Blah.

You won't be able to receive/do the Totems of Hircine quest if you cured yourself of Lycanthropy...

Update: Skjor came back to life in my game, and now HE'S the one giving out quests instead of Farkas (Skjor has dialogue option for work, whilst Farkas doesn't)! This [censored] is trippy yo.

As I said in another post: I went into Skjor's room while he was sleeping, closed the door and killed him. Nobody cared and I committed no crime. He also stayed dead that time. After that Farkas started giving quest again.