Fewer than one in five male workers would take advantage of the proposed six-month paternity leave, according to a poll.
Plans to allow new mothers to transfer the second half of their year's maternity leave would be taken up by 18% of men, the YouGov survey for mobile phone network Orange found.
Concerns about money was the main factor preventing men from taking all the leave (47%), with 27% saying they would not take any time off when the new laws come in to effect from April next year.
The poll found 15% of working men believed they were too vital to the business to be absent for six months, while 3% said senior management were actively against it.
More than three quarters of men 79% said they would make use of a flexible working arrangement if their employer encouraged it.
However 30% said they lacked the necessary support from their senior manages and colleagues, with just 10% currently practising flexible working.
Orange UK spokesman Martin Lyne said: "Businesses need to address this demand or they risk losing valuable members of staff and future revenues. It is surprising how few employers encourage flexible working schemes, especially when there is so much technology to enable it."
He added: "In today's modern working environment, it is right that businesses enable male employees to take their full paternity leave. And it does not have to mean huge sacrifices by either party. The mobile technology which currently exists can empower staff to redress their work-life balance for their staff and enable new fathers to spend time with their families."