Jos. A. Bank shares fell 5 percent, while Men's Wearhouse shares were down 7 percent in midday trading.
(Read more: Unlucky 13? One of Men's Wearhouse's challenges)
The company offered to buy Men's Wearhouse in September for $48 per share, but was swiftly rebuffed as the offer was deemed "inadequate."
Jos. A. Bank did not disclose on Thursday the amount by which it was willing to raise the offer, saying it would first like to conduct limited due diligence to determine a justified increase.
(Read more: We felt government shutdown, says Wal-Mart US boss)
The company said it would cancel its proposal by Nov. 14 if Men's Wearhouse did not enter into discussions.