Anelka opened his Albion account with two goals against Puskas FC Academy this week and Brunt revealed the quiet Frenchman has made his presence felt in the squad.
Brunt said: "Of course, you get excited. When you see a name like that coming to your club you want to play with him and see how he does, and you want to ask him questions about where he's been before.
"It's interesting to ask him questions. Me and Gareth McAuley had 15 minutes with him this week. It was just the three of us in the pool at the hotel the other day.
"We were chatting about football and stuff and talking about where he'd played. It's interesting to learn about other footballing cultures and places he's been.
"With the stuff he has achieved in his career we can learn stuff from him but, on the pitch, he is your team-mate."