Brady, head of youth development, is among the names linked with the Republic of Ireland job but Wenger hopes he will remain at Arsenal.
"I would see that as a loss because he started to produce players now and we have the stability at youth level as well," said Wenger.
"I like to speak to Liam about football because he has a good assessment of players, and a very fair one. He does not get carried away.
"He sees a similar football to my football. I don't know whether it will happen or not. I hope it will not happen."