Acoustic echo cancellers have problems in estimating room transfer functions (TFs) for acoustic echo paths when the conditions are noisy in the acoustic space. In this article, the possibility of estimating the room TFs is investigated by taking a time-frame-averaged cross spectrum(CS) between the input signals and error signals, which are composed of echo signals through the echo path and the surrounding noise. First, the short-time Fourier transforms (STFTs) and cross spectrum for both the input and error signals are taken. The TFs can be estimated from the ratio of the CS to the power spectrum of the input signal, since it can be expected that the time-frame-averaged CS components between the input signal and the surrounding noise will be zero. It was reconfirmed by computer simulation that the echo signals can be suppressed as the averaging process goes on, even in noisy conditions. The room TFs could be estimated as long as the S/N ratio was about 10 dB. This STFT-CS method requires more calculations than a time domain method, such as the RLS method; however, it can be implemented using general purpose FFT boards. Adaptation for rapid TF changes is going to be investigated in the near future.