Details of the plot have not been revealed but The Wrap reports that the American Hustle director has "already had multiple offers for the project sight unseen".
There are no details on which TV networks are involved.
It is thought it will be a limited series run.
It is the second attempt at TV for Russell, who has been nominated for five Oscars and was behind Silver Linings Playbook, American Hustle and Joy.
In 2014 he pulled out of a US TV drama he was set to make, a month after it was commissioned.
The Oscar nominee had co-written ABC's The Club, a drama set in a private country club. No reason was given for his departure.
It is not the first time either of the acclaimed actors has appeared on TV - De Niro and Moore guest-starred in the TV show 30 Rock.
Moore started her career on TV in the soap opera As the World Turns and won an Emmy in 2012 for her performance in the HBO TV movie Game Change, in which she played Sarah Palin.
De Niro is due to be seen soon in the Bernie Madoff HBO TV movie The Wizard of Lies.
De Niro worked with Russell on Silver Linings Playbook, for which he got a best supporting actor Oscar nomination. He also made an appearance in American Hustle.
The double Oscar-winning actor is due to receive a lifetime achievement award at the start of the Sarajevo Film Festival on Friday 12 August.
"We are honoured to have Robert De Niro as the first recipient of the Honorary Heart of Sarajevo - Lifetime Achievement Award," said director Mirsad Purivatra.
He will also present Martin Scorsese's digitally restored Taxi Driver, in which he starred, to celebrate its  40th anniversary.
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Oscar-winning actors Robert De Niro and Julianne Moore are teaming up with writer and director David O Russell for a TV show.