To reduce channel acquisition overhead, spatial, time, and frequency-domain channel extrapolation techniques have been widely studied. In this paper, we propose a novel deep learning-based Position-domain Channel Extrapolation framework (named PCEnet) for cell-free massive multiple-input multiple-output (MIMO) systems. The user's position, which contains significant channel characteristic information, can greatly enhance the efficiency of channel acquisition. In cell-free massive MIMO, while the propagation environments between different base stations and a specific user vary and their respective channels are uncorrelated, the user's position remains constant and unique across all channels. Building on this, the proposed PCEnet framework leverages the position as a bridge between channels to establish a mapping between the characteristics of different channels, thereby using one acquired channel to assist in the estimation and feedback of others. Specifically, this approach first utilizes neural networks (NNs) to infer the user's position from the obtained channel. {The estimated position, shared among BSs through a central processing unit (CPU)}, is then fed into an NN to design pilot symbols and concatenated with the feedback information to the channel reconstruction NN to reconstruct other channels, thereby significantly enhancing channel acquisition performance. Additionally, we propose a simplified strategy where only the estimated position is used in the reconstruction process without modifying the pilot design, thereby reducing latency. Furthermore, we introduce a position label-free approach that infers the relative user position instead of the absolute position, eliminating the need for ground truth position labels during the localization NN training. Simulation results demonstrate that the proposed PCEnet framework reduces pilot and feedback overheads by up to 50%.