No it's not. When a phone is on standby, the microphone circuit is disabled.
I suspect that you've heard an exaggerated version of the true statement that a phone, on standby, can be used to track your movements.
A mobile phone on standby periodically sends out a signal which effectively says, "I am here". (This is an esential part of the way that a cellular network operates. When somebody calls your number, the signal isn't sent to every transmitter in the country; it's only sent to the ones which are near to you). So, theoretically at least, it's possible that 'they' can track your movements from these signals.
In practice, the system only routinely keeps a record of your phone's location when you turn it on (when it always sends out a location message) and when you make a call. However, it would still be possible for the security services to arrange for all location signals, for a particular phone, to be logged and thus track your movements.
Chris