The 21-year-old has scored five times for the La Liga side this season, including three in the league, which is already more than his total for the 2012-13 season.
His current deal will expire in 2015, but Urrrutia is confident that the Spaniard will sign a fresh contract.
"He has asked me to postpone solid negotiations about his renewal until the end of the season, because he doesn't want it to be like a soap opera. Also, he has a personal aim of recovering the sensations he didn't have last season," he told reporters at a press conference.
"Iker has told me that since he came here, as a 12-year-old, he's been delighted. I don't think there's any need for concern. He's a sincere person who Athletic value highly and that conversation has given me calm. My feelings are positive and I'm optimistic."
Muniain has been with Bilbao since 2005.