Both midfielders were sent out on loan last term, van der Gun to Willem II and Obodai to Belgian outfit Germinal Beerschot Antwerpen.
Obodai was expected to stay GBA for next season, but Koeman was impressed with what he saw at the tail-end of last term and offered him the chance to return to Holland.
Van der Gun was seen as a bright prospect in Amsterdam a few years ago, but injuries halted his progress.
He shined at Willem last term and will be given one final chance to prove himself at Ajax.
"Cedric was not 100 percent fit when I became coach," Koeman told Ajax`s website.
"He will get a chance but if I think that during training that his chances are small, we will sit down again.
"Obodai made a good impression at the end of last season, therefore for this reason I cleared a place for him for pre-season."
In other news, Heracles have bolstered their squad for next term with the capture of former Ajax winger Darl Douglas.
The 24-year-old was deemed surplus to requirements at the Amsterdam ArenA and opted to look for a new club after failing to turn his loan spell at Haarlem into a permanent arrangement.
Heracles have decided to take a chance on the Surinam-born winger, who has been handed a one-year contract.
