Omega Supreme didn't have any desire.
He was quiet. Did his job. Sought Cosmos with the same passion one would have for filling up a gas tank when there's still a good five gallons left. Cosmos told him nothing. The Autobot base buzzed about it but they all knew Cosmos wasn't quite the same as they were, so they figured that this was another one of his peculiarities.
It was as silent a relationship as one could have. All Omega cared about was revenge, and hearing him talk about it day in and day out got boring quickly. They ended up playing a lot of radio - any country, any place.
Cosmos mostly liked North American Radio. Omega preferred Israeli. It was a holdover from being stationed in the Middle East for so long. Who knows, it just so happened that Omega wouldn't put up with anything Cosmos liked for long periods of time. He was a pushy giant.
It might be why they eventually went their separate ways. As Whitney used to say "I'd rather be alone than unhappy." Omega was downright impossible to get along with, and it seemed to be a deep commentary on Cosmos' general incompatibility with others that THIS was the only type of machine who found him attractive...and it still didn't work out.
He spent a lot of time alone as it was. It was probably better this way.