Norris spoke on Tuesday of plans for a show in the NT's temporary theatre that was "very focused on disabled issues".
He added he was also in talks with "senior writers" about a play on the main Olivier stage addressing similar themes.
Norris was speaking at a public debate on diversity in UK theatre at the NT in London.
Act for Change, which organised the event, revealed statistics that showed over the Easter weekend only one actor with a "visible disability" had been noted across all theatre sectors, (the West End, regional and subsidised). That had been at the National Theatre.
Interviewed on the Olivier stage, Norris said he was considering whether to introduce quotas to improve diversity within the organisation.
"There is a big argument about whether there should be quotas. Across this year we will be testing that to see how desirable it is," he said.
"Our policy is quite simply to reflect this city and this country. That means in terms of gender, BAME [black, Asian and minority ethnic] and disabled. That's not a difficult policy."
Norris said that in 2014/15 the National's BAME on-stage figure was an unusually high 33% - driven in part by shows such as Behind the Beautiful Forevers and Here Lies Love. He said his aim was for 20% in any given year.
He admitted that it was "much harder" to achieve the same figures in permanent backstage staff.
Pressed on the issue of quotas, he said: "The last thing I'm saying is no.  What I want is for this community to represent the country accurately and if that's the best way of doing it then, yes - why not?"
The Act for Change debate was chaired by Shami Chakrabarti, head of civil rights group Liberty.
Panellists included actors Adrian Lester and Cush Jumbo, director Phyllida Lloyd, critic Mark Lawson, shadow culture secretary Chris Bryant and Jenny Sealey, coÂ­â€

The 54-year-old was convicted of two counts of common assault against the boys, aged 14 and 15, in a food store in north London, in October 2014.
One boy had been trying to pass Joyce in a narrow aisle and after an exchange of words was knocked to the floor.
Joyce will be sentenced at Westminster Magistrates' Court on 27 May.
The former Labour MP had claimed he was performing a "citizen's arrest" at News & Food Express in Chalk Farm and asked the shopkeeper to call police.
The attack happened close to the drinks fridge at about 21:40 BST on 17 October and was filmed on the store's CCTV.
Joyce "flung" the 14-year-old boy to the floor and held him down by the throat, the court heard.
"He started shouting in my face. I remember begging him to leave me alone," the boy said.
His 15-year-old  friend was elbowed and winded while trying to help and both boys then fled the shop, the court was told.
Shopkeeper Ali Fahan said: "I told the man to let him go because he was crying."
Giving evidence, Joyce insisted he had overcome his battle with alcohol after a string of previous convictions.
The court heard that he assaulted politicians in the House of Commons bar in 2012, which led to his resignation from the Labour Party.
He said: "I have a background as a judo player. I was conscious I didn't want to over-act."
The former army major told the court he felt threatened when the boys walked by because one was shouting and swearing and had taken an "aggressive" stance.
Joyce said he put his hand out to stop the teenager knocking over a supermarket shelf but it fell anyway.
Delivering his verdict, District Judge John Zani said: "In my view, you underplayed the violence you meted out to these young men and wanted the police called so as to justify your actions.
"You readily told police, incorrectly, that [one boy] head-butted you for no reason."
He said all sentencing options including imprisonment would be considered.
Joyce is not standing in the general election and has been released on conditional bail until sentencing.
National Theatre boss Rufus Norris has said he hopes to stage more work that will focus on the issue of disability.
[NEXT_CONCEPT]
Former Falkirk MP Eric Joyce has been found guilty of assaulting two teenage boys in an "unjustified and unprovoked" attack in a shop.