The 33-year-old skipper only put pen to paper on a new 24-month deal last summer and has been an integral part of the Reds' title challenge this term.
Though talks are expected to take place, Liverpool's managing director Ayre insists nothing has happened as of yet.
"No, absolutely not. It is not a discussion we have had," Ayre said when asked whether a new contract had been agreed.
"But it is not because it isn't a discussion we won't have.
It won't be a difficult conversation, but it is not one we've had recently
"He is part of the heartbeat of this club and, as long as Steven wants to be here and we want him to be here, it won't be a difficult conversation, but it is not one we've had recently."
Gerrard will be hoping to steer Liverpool to their ninth consecutive league victory against West Ham this afternoon (4pm).
The Reds could overhaul Chelsea at the top of the table with a win.