The offer, worth £40m, was made after the initial £25m bid was rejected by the club.
Wissa is reportedly eager to join Newcastle before the transfer window closes on September 1, and has expressed his frustration with the situation.
Last week, Wissa removed all association with Brentford from his social media accounts, and has also held talks with the club's owner, Matthew Benham, to make clear his intention to leave for Newcastle this month.