The Stoke City forward is due to return to action for Ireland in the second leg of the sides' Euro 2016 playoff clash on Monday, and Begovic has admitted that he is all too aware of Walters's qualities having played with the striker at the Britannia.
"I expect a lot from Jon. Jon's a good quality player and he's going to strengthen their side, but we're trying to prepare as much as possible and it would be nice to get one over him," said Begovic, according to talkSPORT.
"I will speak to some of the defenders in our team about Jon. He's a good quality player and a seasoned pro that has played in the Premier League for a very long time. His quality is there for all to see.
"I'm sure he'll be excited for about the game, but I also think we'll be ready for his qualities and try to limit him as much as possible."
The Republic welcome the visit of Bosnia to the Aviva Stadium with the sides finding themselves tied at 1-1 after the first leg.