The months of Hajj are Shawwâl, Dhû al-Qa`dah and ten days of Dhû al-Hijjah.
It is perfectly permissible for a Muslim to perform `Umrah during these months.
However, if that person had intended to perform Hajj Tamattu` (hajj and `Umrah combined) and then returns home after performing `Umrah, his Tamattu` status will cease.
In other words, when he comes back later for Hajj, he will simply be making Hajj by itself (Hajj Ifrâd) with a new ihrâm. Therefore, he will not be obligated to slaughter an animal during Hajj because he did not perform Hajj and `Umrah together. Instead he performed `Umrah on its own and Hajj on its own.
He should note that when he returns to perform Hajj, it will be obligatory for him to enter into a state of ihram before passing the mîqât. He may not postpone entering into ihrâm until after he reaches Mecca.