Rai had expressed his readiness to "disclose all truths" regarding the crime.
"We have filed our reply and have said that we don't have any objection in making Rai an approver provided that he reveals all the truth in connection with the case," said a CBI official.
Rai, one of the accused in the case, had last month told the court that he wanted to turn an approver.
Expressing his desire to turn approver, Rai had said he wanted to "disclose all truths" as he had taken part in Sheena's killing by strangulation and was present at the time of the murder in 2012.
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Recording his statement before a special CBI court then, Rai said he was under "no pressure, threat or coercion" to reveal the facts in the case and was "repentant" about his act.
Rai was the first to be arrested in the case in August 2015, taking the lid off the murder, after he was picked up in connection with an arms case.
Rai last year had recorded his confessional statement before the magistrate under the provisions of section 164, which unlike the police statement, is admissible in the trial.
Indrani, her former husband Sanjeev Khanna and Rai had allegedly strangled Sheena (24), Indrani's daughter from an earlier relationship, inside a car in April 2012.
The trio were arrested in August last year while Indrani's husband and former media baron Peter Mukerjea was arrested in November. According to CBI, Peter was part of the murder conspiracy.
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Meanwhile, the defence lawyers told the court that they wish to file their replies on CBI's application, in which the investigative agency has said it does not have any objection in Rai becoming an approver.
The court then directed the defence lawyers to file their replies on June 9 and also said it would decide on whether to make Rai approver in the case on that day.