The officers, who are being backed by the Police Federation, claim they are owed money dating back almost 20 years.
Their case against the PSNI follows a landmark court ruling on UK holiday pay rules in 2014.
According to BBC Radio Ulster’s Stephen Nolan show today, the 2014 court ruling was made in a case known as Bear Scotland v Fulton, when judges decided that employees who were regularly required to work overtime should get extra holiday pay.
Some police forces in Great Britain have already settled claims with officers.
The Police Federation in Northern Ireland is representing about 1,300 officers in the legal action against the PSNI.
A smaller group of officers are taking a separate case.
The claims are retrospective and lawyers have suggested they could stretch back to 1998 when the Work and Pay Regulations were introduced in the UK.
In a statement to the Nolan Show, the PSNI’s deputy chief constable said: “At a time of austerity, I must manage scarce resources prudently so as to best protect the people of Northern Ireland.
“It is perfectly understandable that PSNI officers and staff should seek to avail themselves of their entitlements in relation to overtime and holiday pay.
“However, there are difficult points of law which mean that I would be failing my responsibilities if I didn’t seek clarity in the courts, especially when the potential sums of money at stake are very large and would have direct operational impact upon policing in Northern Ireland.”