Can We Do ‘Umrah During the Months of Hajj?
Question

Is it permissible to do ‘Umrah during the months of Hajj, on the basis that I will not do Hajj in the same year? For example, if I go to Makkah about half a month before Hajj, and I do the rituals of ‘Umrah, then I leave – is that permissible?
Praise be to Allah.‘Umrah in the months of hajj
It is permissible to do ‘Umrah during the months of Hajj , and there is no difference of opinion amongst the scholars concerning that. And it makes no difference whether you intend to do Hajj in the same year or not. 
The Prophet’s ‘Umrahs
The Prophet (peace and blessings of Allah be upon him) did ‘Umrah four times, all of which were in the month of Dhu’l-Qi’dah, which is one of the months of Hajj, which are Shawwal , Dhu’l-Qi’dah and Dhu’l-Hijjah . And he did not do Hajj except along with his last ‘Umrah, in the Farewell Pilgrimage. 
Al-Bukhaari (4148) and Muslim (1253) narrated from Anas (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) did ‘Umrah four times, all of them in Dhu’l-Qi’dah except for the one which he did with his Hajj. 
His ‘Umrah from al-Hudaybiyah or at the time of al-Hudaybiyah was in Dhu’l-Qi’dah, his ‘Umrah in the following year was in Dhu’l-Qi’dah, his ‘Umrah from Ji'irranah when he divided the spoils of Hunayn was in Dhu’l-Qi’dah, and his ‘Umrah which he did with his Hajj (was also in Dhu’l-Qi’dah).” 
Al-Nawawi (may Allah have mercy on him) said in his commentary: 
“The conclusion we draw from the reports of Anas and Ibn ‘Umar is that they both indicate that (the Prophet (peace and blessings of Allah be upon him)) did four ‘Umrahs. The first was in Dhu’l-Qi’dah in the year of al-Hudaybiyah, 6 AH, when they were prevented from going further so they exited ihram, but this was counted as an ‘Umrah for them. The second was in Dhu’l-Qid’ah in 7 AH, which was to make up for the previous year. The third was in Dhu’l-Qi’dah of 8 AH, which was the year of the Conquest (of Makkah). And the fourth was with his Hajj, when he entered ihram for it in Dhu’l-Qi’dah but did the actions of ‘Umrah in Dhu’l-Hijjah.” 
And he said: 
“The scholars said that the Prophet (peace and blessings of Allah be upon him) did ‘Umrah in Dhu’l-Qi’dah because of the virtue of this month and to go against the ideas of the Jahiliyyah, because they used to think that this was one of the worst of evil actions. 
So he (peace and blessings of Allah be upon him) did it many times in these months to make it explicitly clear that this was permissible and to demonstrate clearly that the beliefs of the Jahiliyyah were false.”
For more about ‘Umrah, please see these answers: 34744 , 97227 , and 34188 .
And Allah knows best.