According to journalist Rudy Galetti, the 26-year-old is the newest star connected this summer with a move to the Saudi Pro League.
Al-Nassr is looking for a new attacker who was previously linked to Luis Diaz in Liverpool, although that deal would seem to be them.
The club now discusses internally how the deal for Pulisic to get over the line and consider using Aymeric Laporte in a possible deal.
However, it is still to be seen whether Pulisic would be willing to exchange the Serie A for Saudi Arabia and join Cristiano Ronaldo and Sadio Mane.