Performing عمرہ in Dhul Hijjah is permissible according to all scholars, as there is no prohibition against عمرہ in any month of the year. The first ten days of Dhul Hijjah are among the best days of the year, and performing عمرہ in them is virtuous. The question that generates more discussion is performing عمرہ after completing حج, during the remaining days of Dhul Hijjah.
Sheikh Ibn Baz stated that performing عمرہ after حج is permissible, as demonstrated by نبی کریم's instruction to Abdur-Rahman to take his sister Aisha to Tan'eem for عمرہ after their حج was complete. This occurred during the Farewell Pilgrimage in Dhul Hijjah. He considered this a clear evidence that عمرہ in Dhul Hijjah — even after حج — is valid and carries reward.
Sheikh Al-Albani, however, noted that Aisha's عمرہ was a special case — she was distressed because she had not been able to perform a separate عمرہ (having been instructed to combine حج and عمرہ as qiran). نبی کریم accommodated her specific situation. He pointed out that نبی کریم himself and the rest of the companions did not perform عمرہ after حج. Based on this, Al-Albani considered it better to follow نبی کریم's own practice of not performing a separate عمرہ after حج, though he did not prohibit it.