The two firms have been shortlisted for the second stage of bidding for the business, said Bloomberg, citing two people familiar with the matter.
The sale is managed by banking group HSBC’s Saudi unit, said the sources.
Kudu, which operates 200 restaurants, is expected to be valued at between SAR1.5bn ($400m) and SAR2bn.
One of the people said that Dubai-based Abraaj also plans an initial public offering of oil and gas services provider Stanford Marine Group, which could come as soon as in the first quarter of 2014.
Last week Abraaj backed Moroccan pharmaceutical products provider Steripharma.
Copyright © 2013 AltAssets