Quantum key distribution (QKD) protocols are becoming more and more investigated by researchers and implemented in practice. In such systems, in addition to detecting eavesdroppers, it is essential to determine the location of the malicious party along the transmission channel, to remove or circumvent the threat. Although optical fiber is the predominant transmission medium for QKD, existing sensing techniques, mostly based on optical time domain reflectometry, are often expensive and require complex additional hardware. This paper proposes an alternative approach for the localization of eavesdroppers along an optical fiber in a BB84 QKD architecture, without the need for additional optoelectronic equipment. In particular, we present an analytical method based solely on Quantum Bit Error Rate (QBER) statistics to determine the position of the attacker along the channel, reducing the physical cost to zero. The theoretical framework is validated through various simulations carried out using the Qiskit library. The results highlight the feasibility of our method in the case of intercept-resend attacks, achieving a maximum relative prediction error of 6.1%.