The pilgrim is not obliged to offer an udhiyah and it is not prescribed for him to slaughter it in Makkah. Rather what is required and prescribed in his case is to offer the hadiy. If he does Hajj Tamattu’ or Qiraan, then he must offer the hadiy, which is a sacrifice which must fulfil the same conditions as the udhiyah, because offering a sacrifice is obligatory for those who are doing Tamattu’ or Qiraan. If he cannot afford to offer a sacrifice then he must fast for ten days, three days during Hajj and seven days after he returns to his homeland, as Allaah says (interpretation of the meaning):
“and whosoever performs the ‘Umrah in the months of Hajj, before (performing) the Hajj, (i.e. Hajj-at-Tamattu‘ and Al-Qiraan), he must slaughter a Hady such as he can afford, but if he cannot afford it, he should observe Sawm (fasts) three days during the Hajj and seven days after his return (to his home), making ten days in all”
For the one who is doing Hajj Ifraad, he does not have to offer a hadiy, but he may do so voluntarily. The Prophet (peace and blessings of Allaah be upon him) offered a hadiy of one hundred budnah (camels) during his Hajj.
The point is that whether his family offers an udhiyah on his behalf or not, it is not recommended for him to offer an udhiyah so long as he is going to go for Hajj.
If the pilgrim leaves his family in his homeland, it is prescribed for him to leave them money so that they can offer an udhiyah.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked: How can a person combine udhiyah and Hajj, and is that prescribed?
He replied: The pilgrim does not offer an udhiyah, rather he offers a hadiy. Hence the Prophet (peace and blessings of Allaah be upon him) did not offer an udhiyah during the Farewell Hajj, rather he offered a hadiy. But if we assume that he is doing Hajj by himself and his family are in his homeland, then in that case he should leave his family enough money to buy an animal and offer it as an udhiyah, so he will be offering a hadiy and they will be offering an udhiyah, because the udhiyah is only prescribed in places other than Makkah, but in Makkah it should be a hadiy. End quote from al-Liqa’ al-Shahri.
And Allaah knows best.