Her absence would be the second major setback for the Auckland tournament in a matter of days, after Juan Martin Del Potro's injury-enforced withdrawal last Saturday.
Ivanovic has been a popular figure in Auckland.
She beat Venus Williams to take the title in 2015 - in one of the best women's finals seen at Stanley Street - but was a surprise first round loser this year to Naomi Broady.
This past year was her worst WTA campaign in more than a decade.
Ivanovic ended the year outside the top 50 for the first time since 2004, and had first round losses at Wimbledon and New York. Ivanovic was also stopped in the third round at the Australian and French Opens, and announced after the US Open that she was taking a break from the WTA tour to rest a wrist injury.
Ivanovic has also made no secret of her desire to start a family, in the wake of her marriage to German footballer Bastian Schweinsteiger in Venice last July.
ASB Classic tournament director Karl Budge said he wasn't sure what Ivanovic's announcement was going to be.
"Like most tennis people, I'll be watching her facebook page on Thursday morning," said Budge, who said he hadn't had any contact with Ivanovic's team since the Serbian posted her cryptic tweet yesterday.
