To sweeten the pot, Men's Wearhouse said it would consider raising the offer to $65 per share if it is allowed to conduct further due diligence, and have access to the retailer's management team.
"We call on the Jos. A. Bank Board to act in the best interests of their shareholders and begin discussions with us immediately," said Men's Wearhouse CEO Doug Ewert in a statement.
Jos. A. Bank was unavailable for immediate comment.
The two companies have been locked in a takeover battle for months.
It all started last year, when Jos. A. Bank made an offer to buy Men's Wearhouse for $2.4 billion. Men's Wearhouse rejected that offer and countered with an unsolicited bid of $55 a share for Jos. A. Bank -- a proposal that was also rejected.
Men's Wearhouse is out of style
It's been a tumultuous few months for Men's Wearhouse, which is under pressure from its largest shareholder, Eminence Capital, to secure a deal.
Last June, the retailer announced the firing of George Zimmer, its chairman, founder and long-time pitchman.
Shares of Jos.A. Bank rose more than 8% in premarket trading while Men's Wearhouse jumped 6%.