Danske Bank has offered about 40% of its employees voluntary redundancy as part of efforts to cut costs against the backdrop of low interest rates.
The bank has offered 8,000 staff, mainly in the bank's personal banking and business banking divisions in Denmark, to leave voluntarily.
They have until October 31 to consider the offer, spokesman Kenni Leth said.
Keeping down costs is part of Danske Bank's aim to deliver return on equity of at least 12.5% in 2018, while growth in "digitalisation" also means the bank will need fewer staff, Leth said.
The bank has no specific target for how many positions it will cut, he said. Danske Bank, Denmark's biggest bank, employs 19,400 people.
Danske Bank and other Danish banks have proved relatively resilient in the face of negative interest rates, low oil prices and financial market volatility, which is in contrast to many banks in Europe.
"The low interest rate environment and low growth is challenging the whole sector, and we also need to adjust to that," Leth said.
He said the offer was mainly targeted at employees who were nearing retirement age or otherwise considering other opportunities.