What is the phrase to use about reaching a topic while talking?

Solution 1:

Here's what you might you be looking for,

Come up

: (of an issue, situation, or problem) occur or present itself, especially unexpectedly.

Some example sentences -

‘This issue just keeps coming up again and again.’

‘I'm not even sure that I'd vote on the issue if it were coming up for legalization in my state; there are a lot more pressing economic issues on my mind.’

‘‘Ninety-seven percent of issues that are coming up are localized,’ he said.’

‘It's an old thread, but the same issues seem to keep coming up.’

‘He says the one issue which kept coming up on the doorsteps in the recent General Election campaign was the state of the country's health service.’

(From Oxford)

EDIT

Cascabel has provided a simpler definition of "come up"-

: to be mentioned or talked about in conversation.

(From Cambrigde Dictionary)