Target speaker extraction aims to isolate the voice of a specific speaker from mixed speech. Traditionally, this process has relied on extracting a speaker embedding from a reference speech, necessitating a speaker recognition model. However, identifying an appropriate speaker recognition model can be challenging, and using the target speaker embedding as reference information may not be optimal for target speaker extraction tasks. This paper introduces a Universal Speaker Embedding-Free Target Speaker Extraction (USEF-TSE) framework that operates without relying on speaker embeddings. USEF-TSE utilizes a multi-head cross-attention mechanism as a frame-level target speaker feature extractor. This innovative approach allows mainstream speaker extraction solutions to bypass the dependency on speaker recognition models and to fully leverage the information available in the enrollment speech, including speaker characteristics and contextual details. Additionally, USEF-TSE can seamlessly integrate with any time-domain or time-frequency domain speech separation model to achieve effective speaker extraction. Experimental results show that our proposed method achieves state-of-the-art (SOTA) performance in terms of Scale-Invariant Signal-to-Distortion Ratio (SI-SDR) on the WSJ0-2mix, WHAM!, and WHAMR! datasets, which are standard benchmarks for monaural anechoic, noisy and noisy-reverberant two-speaker speech separation and speaker extraction.