Captain Steven Gerrard recently urged the Merseyside outfit to give the Northern Irishman a fresh deal following his impressive start to his Anfield career.
The former Swansea City boss has led the Reds to the top of the Premier League table with six games left to play in his second season in charge.
However, according to Ayre, the club's stance is to only discuss fresh terms with Rodgers when the time is right.
"It's never been an issue," Ayre told Sky Sports News. "We will have our own dialogue at appropriate time, we will have that discussion. Right now isn't the time.
"We don't want a distraction. That's a private matter. I know Brendan, myself and the owners are all very comfortable with that."
Liverpool currently have a two-point lead over Chelsea, while Manchester City sit four points behind with two games in hand.