Sayyidi wa sanadi Shaykh Mohammad Taqi Usmani (may Allah preserve him) writes,

“Ibn ‘Abidin, the well-known scholar of the Islamic jurisprudence, has mentioned that the people of Makkah (in his days) used to perform ‘umrah in the month of Rajab. Perhaps they believed that performing ‘umrah in this month is more meritorious than in other months. Then Ibn Abidin himself has rejected the authenticity of this practice, because no tradition of the Holy Prophet (Allah’s blessings and peace be upon him) is found to this effect. Conversely Sayyidah ‘Aishah, Radi-Allahu anha, has expressly negated the presumption by saying that the Holy Prophet (Allah’s blessings and peace be upon him)never performed an ‘umrah in the month of Rajab (Sahih Muslim 1:409)

However, Ibn ‘Aibidin has quoted a narration that ‘Abdullah ibn Zubair, Radi-Allahu anhu, completed the renovation of Ka’bah shortly before 27th of Rajab, and as a sign of gratefulness he performed ‘umrah and slaughtered some animals. But this report cannot form the basis of a recognized annual practice, firstly because the report is not very authentic, and secondly because it does not mention that Abdullah ibn Zubair, Radi-Allahu anhu, had adopted it as a continuing practice. At the most, he performed ‘umrah once as a sign of gratefulness on the completion of Ka’bah. It does not mean that he performed it as a characteristic of the month of Rajab. Therefore, performing ‘Umrah in this month is like performing it in any other month and no special merit can be attached to it merely because it has been performed in the month of Rajab.”

Rajab: Islamic months