All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Regarding the virtue of fasting the month of Rajab, the scholars stated that there is no authentic narration which is confirmed from the Prophet indicating that there is any special virtue for fasting all or part of this month. Ibn Hajar Al-Hanbali said in Lataaif Al-Ma'aarif: "With regard to fasting the month of Rajab, no authentic narration can be attributed to the Prophet, nor to the companions of the Prophet which proves this." However, there is a narration from Abu Qilaabah which says, "There is a palace in Paradise for those who fast Rajab." [End of quote]
Therefore, the quote you are asking about is not a narration from the Prophet but rather it is a statement attributed to one of the Taabi'een (the generation after that of the Companions').
Since you write to us sometimes in Arabic, then we will refer you to the Fatwa number 38462 on our Arabic website about fasting in the sacred months.
Allah Knows best.