The two clubs have come to an agreement over a loan fee for the 23-year-old, Sky Sports News understands.
If personal terms between Chambers and Fulham can be agreed, the player could undergo a medical later on Monday.
Chambers agreed a new four-year deal with Arsenal last month, committing his long-term future to the club.
He is poised to join new signing Alfie Mawson at Fulham, whose £15m arrival from Swansea was recently confirmed by the club.
Mawson is currently working back to match fitness following injury, and is expected to be ready by September.
Fulham have also brought in high profile signings in Jean Michael Seri, Andre Schurrle and Aleksandar Mitrovic this summer as they prepare for their first season back in the English top flight.