Reports in England and Romania had claimed that a deal close to £7million was almost complete and that Chiriches would seal a switch to White Hart Lane after the first leg of Steaua's Champions League qualifier with Dinamo Tbilisi this week.
However, it is believed that the deal has been called off by Steaua's owner Gigi Becali, who is currently serving a three-year prison sentence.
"It's a difficult situation for Vlad," Steaua coach Reghecampfs is quoted by Romanian broadcaster Digisport.
"We all decided that if an offer came on, he would leave after the Champions League play-off and I agreed that he should leave, but Gigi [Becali] has decided that he should stay and help us qualify for the Champions League.
"He will have to get over this and he is a boy with an incredible character, but he was affected. I'm still sure in the future he will go to a strong team from abroad."
Chiriches, 23, who has previously been targeted by Milan duo AC and Inter, is regarded as one of the best young defenders in Europe.
Steaua general manager Mihai Stoica added: "There is indeed an offer for Chiriches, the highest ever received in Romanian football.
"But until winter he will not leave under any circumstances. This could be a blow to Chiriches, but he should understand. He owes a lot to Steaua.
"Things are good, we are in qualifying for the Champions League. We are in good shape."