The reality TV star is calling for Alice Marie Johnson, who is serving a life sentence without parole for a non-violent drug offence, to be pardoned.
The 37-year-old also met the president.
Mr Trump tweeted: “Great meeting with @KimKardashian today, talked about prison reform and sentencing.”
The Keeping up with the Kardashians star tweeted earlier on Wednesday: “Happy Birthday Alice Marie Johnson. Today is for you.”
Ms Johnson was convicted in 1997.
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An online petition to grant clemency, started by her daughter, currently has more than 250,000 signatures.
Kardashian West is thought to have been involved in private discussions with Mr Kushner and his wife Ivanka Trump for several months.