The OSCR will carry out the examinations as part of its rolling review of charities north of the border under the Charities and Trustee Investment (Scotland) Act 2005.
Schools to be reviewed include Fettes College in Edinburgh, the High School of Glasgow and Craigholme School, which is also in Glasgow.
The regulator has previously assessed 13 fee-paying schools, of which eight met the required criteria after their first assessment. The other five met the requirements after they were given directions from the OSCR.
David Robb, chief executive of the OSCR, said the review process was an important part of ensuring that charities were seen to be providing public benefit.
"We believe it is right, as agreed by our board in January of this year, that we now proceed to complete our assessment of the remaining schools in this priority group.
"We have reviewed 13 schools so far, to reassure the public that the requirements of charitable status are protected. We look forward to engaging in dialogue with these charities, so that they can demonstrate the benefit they provide and how they address any restrictions."