Mention a former university colleague in a cover letter if we never worked toget...

I recently ran into a former university colleague at a conference. They told me about their current company, and that they operate in the exact field I want to enter. While they couldn't share details due to IP constraints, they did mention great working conditions and told me they are currently hiring.

I am now preparing to apply. Is it appropriate to ask for their consent to mention them in my cover letter? If they agree, what is the best way to phrase it?

I am hesitant because of the advice you gave in a related question. We barely interacted in university and never worked together; at most, they might remember I was a top student in our cohort. They know the company where I now work. Because our conversation was brief and mostly just sparked my own independent research, I want to make sure I don't overstep or look like I am superficially name-dropping.

Note: the application process consists in writing an email to a general address, expressing interest in one of the open positions.

Is it appropriate to ask for their consent to mention them in my cover letter?

Sure, if you ask nicely and give them the option to decline without feeling awkward about it

If they agree, what is the best way to phrase it?

Concise and truthful. For example: "I heard about you from ABC, who is a former university colleague of mine".

In fact you should phrase it first and then ask your college if it's ok to use this specific phrasing in your cover letter. This way, they know exactly what they are agreeing to, which makes the decision a lot easier