PSV have been in contact with City about renewing the defender's loan after last season's success.
The Dutch giants had anticipated a quick decision from City, but PSV chief Marcel Brands has been informed he must wait.
City manager Manuel Pellegrini may perform a U-turn and keep hold of Rekik due to homegrown quota laws in England.
Brands has given City a two-week deadline to make a final decision.
For the big stories and the banter follow us on Twitter: @tribalfootball