The former Netherlands international, 47, has been offered the job and negotiations are at an advanced stage.
It is understood he was the first choice of Palace chairman Steve Parish and informed the south London side they were his preferred option.
De Boer is set to succeed Sam Allardyce, who left after helping Palace avoid relegation from the Premier League last season.
De Boer, who won 112 caps for the Netherlands, has been out of work since he was sacked by Inter Milan in November 2016 after only 85 days in charge.
Between 2010 and 2016 De Boer managed Ajax, winning the Eredivisie four years in a row between 2011 and 2015.
He stepped down days after missing out on a fifth league title to PSV Eindhoven on the final day of the 2015-16 campaign.
De Boer is thought to have impressed the Palace hierarchy with his knowledge of the club and his footballing vision.
It is said the respect and humbleness he showed was striking, especially given how much he achieved as a player.
The ex-Ajax, Barcelona and Rangers defender is understood to have committed to giving players from the existing squad a chance to impress before looking to make new signings.
Palace have invested heavily in recent transfer windows, but will back De Boer and have made him aware of their budget.