Ms Khobragade’s detention on charges of visa fraud and underpaying her housekeeper led to outrage in India, where she is seen as being victimised.
She has denied all the charges and has been released on bail.
India has demanded an apology from the US over her alleged “humiliation”.
But Press Trust of India news agency quoted US sources in New York as saying that the US is gathering more evidence against the diplomat ahead of 13 January, the deadline for her indictment.
The sources said there was no question of dropping the charges against Ms Khobragade or apologising for the arrest.
Ms Khobragade, India’s deputy consul general in New York, was arrested in the city on 12 December on suspicion of visa fraud and making false statements, after being accused of paying her Indian maid below the US minimum wage.
She was handcuffed and strip-searched after a complaint from the maid, Sangeeta Richard.
The diplomat, who has been released on bail, denies all the charges and has in turn accused Ms Richard of theft and attempted blackmail.
Delhi had already ordered a series of reprisals against the US.
Security barricades around the US embassy in the city were removed and a visiting US delegation was snubbed by senior Indian politicians and officials. India is also checking the tax status of Americans working at schools in the country.