Automating requirements quality analysis remains challenging because multiple, often conflicting quality attributes must be balanced while preserving stakeholder intent. Existing Large-Language-Model (LLM) approaches predominantly rely on task-oriented decomposition or implicit aggregation, limiting their ability to systematically surface and resolve cross-quality conflicts. We present QUARE (QUality-Aware REquirements Analysis), a multi-agent framework that takes a project description as input and formulates requirements quality analysis as structured negotiation among five quality-specialized agents: Safety, Efficiency, Green, Trustworthiness, and Responsibility, coordinated by a dedicated orchestrator. QUARE introduces a dialectical negotiation protocol that explicitly exposes inter-quality conflicts and resolves them through iterative proposal, critique, and synthesis. Negotiated outcomes are transformed into structurally sound KAOS goal models via topology validation and verified against industry standards through retrieval-augmented generation (RAG). We evaluate QUARE on five benchmark systems drawn from established RE benchmarks, MARE and iReDev, and an industrial autonomous-driving specification, spanning safety-critical, financial, and information-system domains. Results show that QUARE achieves 98.2% compliance coverage, a 105% improvement over both baselines; 94.9% semantic preservation, a 2.3 percentage-point improvement over the best baseline; and high verifiability, with a score of 4.96 out of 5.0, while generating 25-43% more requirements than existing multi-agent RE frameworks. These findings suggest that, when using capable instruction-tuned models, architectural choices such as quality-dimension decomposition, explicit negotiation, and automated verification may contribute more to output quality than model scale alone.