The South Africa international has shone in the Eagles' midfield this season alongside Mile Jedinak.
But Dikgacoi is out of contract in the summer and has already been approached by a number of clubs from the continent with interest emerging from Germany, France and Spain.
However, there is also strong interest emerging from the Premier League too.
Newly-promoted Leicester are understood to be keen, whilst Newcastle, Hull City, Stoke and West Brom are all believed to be keeping close tabs on him.
Palace look set to offer the former Fulham player a new long-term deal, but they may struggle to match offers from elsewhere.