The move would mean businesses will be allowed to employ an additional 8,000 skilled migrants annually in industries including IT, engineering and education, which according to the paper effectively increases the current cap by 40 percent.
NHS doctors and nurses will be excluded from restrictions to the number of visas granted to skilled non-EU migrant workers, the Home Office has confirmed.
The Home Office said the announcement means that there will be no restriction on the numbers of doctors and nurses who can be employed through the Tier 2 visa route.
I recognise the pressures faced by the NHS and other sectors in recent months.
Such workers will be exempt from the cap on Tier 2 visas, which has been exceeded for six consecutive months.
'Doctors and nurses play a vital role in society and at this time we need more in the UK.
'This is about finding a solution to increased demand and to support our essential national services'.
Health Secretary Jeremy Hunt said the move would "send a clear message to nurses and doctors from around the world that the NHS welcomes and values their skills and dedication", adding: "It's fantastic that patients will now benefit from the care of thousands more talented staff".
He said he would take "think more carefully" about the cap on the number of skilled workers given visas.
But since this quota got filled quickly, the NHS was not able to recruit trained doctors - from India, for example.
"Net migration is falling", said Mrs May's official spokesman.
The cap, introduced by May when she was interior minister, is now set at 20,700 non-EU skilled workers per year.
He has also reportedly proposed a universal immigration system that does not favour European Union nationals after Brexit.
Sunder Katwala, director of the immigration think-tank British Future, said removing medical personnel from the visa cap would be a "sensible move".
"It never made sense to turn away doctors and nurses that the NHS needs".
In an interview with the BBC's Andrew Marr, Javid said he "saw the problem" with the cap that sets a limit for all non-EU skilled workers at 20,700 people a year.
Immigration rules capping the number of foreign medics working in the United Kingdom are reportedly going to be eased to allow the NHS to recruit more staff.
Whether Javid will prove to be a new broom at the home office remains to be seen.