I asked Saeed bin Jubayr about fasting in Rajab, and we were at that time in the month of Rajab. He said, "I heard Ibn Abbas say, 'The Messenger of Allah ﷺ used to fast until we said he would never break his fast, and he used to break his fast until we said he would never fast.'"
سألت سعيد بن جبير عن صوم رجب؟ ونحن يومئذ في رجب فقال: سمعت ابن عباس يقول: كان رسول الله ﷺ يصوم حتى نقول لا يفطر ويفطر حتى نقول لا يصوم.
Muslim narrated it in Sawm (1157: 179) through various routes from Uthman bin Hakeem Ansari, who said, and he mentioned it.It appears that Saeed bin Jubayr's intent by this argument was that fasting in Rajab is neither prohibited nor recommended in itself, but rather it has the same ruling as the rest of the months. No prohibition or recommendation has been established regarding fasting in Rajab specifically. This is what Nawawi conveyed.