´It was narrated that Ibn 'Abbas said:` "The Messenger of Allah would fast until we said he would not break his fast, and he would not fast until we said he does not want to fast. And he never fasted any month in full apart from Ramadan, from the time he came to Al-Madinah."
Related hadith on this topic
Explanation & Benefits
Shaykh Umar Farooq Saeedi
Benefits and Issues:
Rajab is among the sacred months.
And in the light of this hadith, it can be said that the Messenger of Allah (sallallahu alayhi wa sallam) used to fast abundantly in this month.
Or it may mean that, like other months, sometimes he would fast and sometimes he would not.
There is no specific ruling regarding this.
And Allah knows best.
Source: Sunan Abu Dawood – Commentary by Shaykh Umar Farooq Saeedi, Page: 2430