But they rocketed to stardom when one of Russia's television networks unveiled a documentary ode to their friendship.
Three thousand visitors came to see the pair on one day alone at New Years.
"The situation is really weird. For three years running we have fed Amur a huge number of goats, rabbits, roosters and rams," said Dmitry Mezentsev, the general director of the Primorsky Safari Park. "My only explanation is that this couldn't have happened without interference of the higher power. Amur has never rejected prey before."
The friendship started after the goat chased the tiger out of his sleeping place, and claimed the comfortable area for his own.
Amur, apparently confused that the goat was not properly submissive, went to sleep on the roof.
The zoo has given up feeding goats to the tiger.
Timur and Amur enjoy playing with a ball, one snatching it from the other and running away, as the other tries to catch up.
They are prepping for the 2018 World Cup in Russia, Mezentsev joked.