It is permissible to perform 'Umrah during the months of Hajj
حَدَّثَنَا نَصْرُ بْنُ عَلِيٍّ الْجَهْضَمِيُّ، حَدَّثَنَا أَبِي، حَدَّثَنَا شُعْبَةُ، عَنْ أَيُّوبَ، عَنْ أَبِي الْعَالِيَةِ، الْبَرَّاءِ أَنَّهُ سَمِعَ ابْنَ عَبَّاسٍ، - رضى الله عنهما - يَقُولُ أَهَلَّ رَسُولُ اللَّهِ صلى الله عليه وسلم بِالْحَجِّ فَقَدِمَ لأَرْبَعٍ مَضَيْنَ مِنْ ذِي الْحِجَّةِ فَصَلَّى الصُّبْحَ وَقَالَ لَمَّا صَلَّى الصُّبْحَ " مَنْ شَاءَ أَنْ يَجْعَلَهَا عُمْرَةً فَلْيَجْعَلْهَا عُمْرَةً " .
Ibn 'Abbas (Allah be pleased with them) 'is reported to have said: The Messenger of Allah (ﷺ) put on Ihigm for Hajj. When four days of Dhu'l-Hijja were over, he led the dawn prayer, and when the prayer was complete, he said: He who wants to change it to Umra may do so.