In some cases women can loose their sex drive could it be the other way around?

It all depends on the woman. But yes, some women have an increase in sex drive after menopause.

From personal experience, and some web search, it appears that loss is more common but more or same is possible also.

If you look at what is going on it can go either way. Your body is shutting down it's baby making gear. We're out of eggs, no more quiches, we're done, you don't have to go home but you can't stay here. This is mainly done by changes in hormones. The problem is that most hormone don't just have a single effect but can multiple varied effects. The way the body does the menopause and its reactions to it are unique to each person. With that said there are broad strokes that can be used to generalized the response.

TL;DR: Yes it is possible.

Menopause means no more babies, so a woman's interest in sex might increase knowing that she no longer has to worry about birth control.