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Wa`alaykum as-salamu wa R ahmatullahi wa B arakatuh. 

In the Name of Allah, Most Gracious, Most Merciful. 

All praise and thanks are due to Allah, and peace and blessings be upon His Messenger. 

Brother, we really appreciate your forwarding this question to us, and we commend your desire to become well acquainted with the teachings of Islam. May Allah help us all keep firm on the straight path. Ameen. 

It should be clear that a person who is offering the pilgrimage cannot do the `Umrah on these days. However, a person who is not doing the pilgrimage may offer the `Umrah at any time, even on the day of `Arafat, or on the Day of Sacrifice. 

As regards to your question, we'd like to supply you with the following fatwa:

If the author means that a person who is offering the pilgrimage cannot do the `Umrah on these days, then he is correct. Many pilgrims take the opportunity of being in Makkah in order to do `Umrah after the Hajj. This particularly applies to those who opt for the ifrad method of Hajj. These pilgrims should wait until the 14th of Dhul-Hijjah when they should go out to At-Tan`eem or any point at the boundaries of Al-Haram area where they should then enter into the state of ihram, making their intention to do the `Umrah, and return to Makkah to fulfill its duties.

However, a person who is not performing the Hajj may offer the `Umrah at any time, even on the day of `Arafat, or on the Day of Sacrifice. Take, for example, the case of a person traveling from Europe or Africa to Pakistan, India, or any Eastern destination. He can make a stopover at Jeddah for one day or a few hours, during which he wishes to do the `Umrah. There is nothing to prevent him from doing so, as long as he has the necessary permission ( the appropriate visa). If such a person arrives in Jeddah on the day of `Arafat, he may go ahead and do the `Umrah. There is nothing to prevent him from doing so.

Excerpted, with slight modifications, from www.islamicity.com. 

Allah Almighty knows best.