The Republic of Ireland international, 24, made 36 appearances for the Canaries last season after joining from Hull for £7m in July 2015.
He could not prevent them going down and has been linked with Premier League champions Leicester after scoring against Italy at Euro 2016.
"We'll wait and see what happens with that situation," Neil told BBC Norfolk.
"But we're certainly in no rush to move Robbie, or anything like it.
"I think some people questioned the fee when I bought him, but I'm pretty sure nobody's suggesting that's a bad fee now."
Neil has made just one summer signing so far, with Spain Under-19 winger Sergi Canos moving to Carrow Road from Liverpool for an undisclosed fee, believed to be about £2.5m.
"We'll have (more) business done before the window ends," added Neil.
"We're making every effort to get things done, but what you can't allow to happen is you can't be bullied by price.
"You can't be bullied by some tactics that other clubs will deploy at times, so what we've got to do is be strong, brave and make sure we see it through and eventually get the bodies in, which we will."
Norwich City boss Alex Neil says the Championship side are "in no rush" to sell winger Robbie Brady.