According to the Football411 website, Ertugral's request has thus led to speculation that the fiery Turk will remain in charge of the Urban Warriors come next season.
Ajax ended their PSL campaign in 14th place, just three points clear of Chippa United following their 3-0 win over Golden Arrows at Athlone Stadium on Saturday.
Ertugral, who came in to replace Jan Versleijen barely a month ago, steered the Cape outfit to two wins and two draws after focusing on improving the atmosphere at the relegation-threatened side and raising team morale.
However, Ajax Amsterdam publicly revealed their annoyance at the way their South African counterparts managed their affairs following Ertugral's re-appointment at Ikamva.
The 53-year-old tactician, though, shrugged off the Dutch giants' concerns, but now expects everyone involved with Ajax - home and abroad - to work in unison going forward.
"The whole management, everyone here, and the Ajax Amsterdam contingent need to sit down. We can't have this situation again," Ertugral said. "Everybody must sit together and plan how we will get out of this, but I feel now that everybody is on board - the players and the management."