Earlier this month, Spurs had come close to agreeing a deal for highly-rated Chiriches, only for imprisoned Steaua owner Gigi Becali to call off the deal.
Reports now claim that Spurs have returned with a different offer which includes the whole deal being paid for by January 2014.
Steaua sources claim that the near-£8million deal is in place and could be confirmed over the weekend.
Asked about one of his star men, Romania coach Piturca is quoted by Adevarul Sports as saying: "From what I know, in the next few days Chiriches will sign for another team."
Chiriches, who spent time with Benfica as a youngster, has emerged as one of the top young defenders in Europe and Milan duo AC and Inter had both tried and failed to sign him in the past 12 months.