Is ‘Umrah in Rajab Recommended?
Question

Is there any particular virtue in performing ‘Umrah in the month of Rajab?
Praise be to Allah.Is There any hadith about offering ‘Umrah in Rajab? 
There is no report from the Prophet (peace and blessings of Allah be upon him) – as far as we know – to suggest that there is any particular virtue in performing ‘Umrah in the month of Rajab , or that it is encouraged. Rather it is proven that there is a particular virtue in performing ‘Umrah in the month of Ramadan , and in the months of Hajj, which are Shawwal, Dhu’l-Qa’dah and Dhu’l-Hijjah. 
There is no report to prove that the Prophet (peace and blessings of Allah be upon him) performed ‘Umrah in Rajab , rather that was denied by ‘Aishah (may Allah be pleased with her), who said: The Messenger of Allah (peace and blessings of Allah be upon him) never performed ‘Umrah in Rajab. (Narrated by al-Bukhari, 1776; Muslim, 1255)
Is Singling out Rajab for ‘Umrah Permissible?
Something that has been introduced into the religion is what some people do, namely singling out the month of Rajab for ‘Umrah, because no one should single out a specific time for doing an act of worship unless that has been prescribed in Shari’ah. 
Ibn al-‘Attar, the student of al-Nawawi (may Allah have mercy on them both) said: 
What I have heard about the people of Makkah, may Allah increase it in honour, is that they are accustomed to performing ‘Umrah a great deal in Rajab . This is something for which I know of no basis, rather it is proven in the hadith that the Prophet (peace and blessings of Allah be upon him) said: “ ‘Umrah in Ramadan is equivalent to Hajj.” End quote.
Shaykh Muhammad ibn Ibrahim (may Allaah have mercy on him) said in his Fatawa (6/131): 
“With regard to singling out some days of Rajab for any kinds of ziyarah etc, there is no basis for that. Imam Abu Shamah stated in his book al-Bida’ wa’l-Hawadith that performing acts of worship at specific times which were not prescribed by Islam is not right, because no time is better than any other, except times when it is prescribed to perform a certain kind of worship, or a time when all kinds of good deeds are better than at other times. Hence the scholars denounced the singling out of the month of Rajab for performing ‘Umrah a great deal.”
But if a person goes for ‘Umrah during Rajab without believing that there is any special virtue in that, but it just so happens that it is easy for him to travel at that time, there is nothing wrong with that.
And Allah knows best.