In open-loop Wire Arc Directed Energy Deposition (WA-DED), the contact tip–to–workpiece distance (CTWD) is commonly adjusted between layers using expected average values of layer height derived from experimental data. However, due to complex thermal effects, mismatches between expected and actual process conditions lead to uncontrolled CTWD fluctuations, which can cause process instabilities, arc extinction events, and geometric defects. Reliable online estimation of CTWD is therefore essential for process monitoring and for enabling future closed-loop control strategies. Existing CTWD monitoring approaches typically rely on vision-based or acoustic emission systems, which are costly or sensitive to industrial noise. This work proposes a data-driven method for online CTWD estimation using only welding current and voltage, signals already available in industrial WA-DED systems. By avoiding additional sensors, the approach enables low-cost, robust, and real-time CTWD estimation suitable for direct industrial deployment. Several machine learning and deep learning models are evaluated, with particular focus on Ridge Regression, Support Vector Regression and a 1-dimensional convolutional neural network. Experimental results show that the deep learning approach provides higher estimation accuracy and robustness compared to conventional machine learning methods, while remaining suitable for real-time implementation. The proposed method offers a practical solution for CTWD monitoring in WA-DED and represents a step towards intelligent process supervision and control in wire-based additive manufacturing.