A leaked Government report on the effect on Britain of the EU's policy allowing free movement of people suggests a cap could cut net migration from EU countries by 30,000 from the current 106,000 a year.
The document also suggests blocking EU immigrants from claiming benefits or tax credits for their first five years in the UK.
The paper emerged just weeks before restrictions on the movement of Bulgarian and Romanian citizens are lifted at the end of the month.
The proposals would mean professionals and highly-skilled migrants from countries such as Germany, Holland or Austria could only move to the UK if they had a job offer. Lower-skilled workers would be allowed to settle if they had jobs on an approved list of occupations for which there was a national shortage.
The leaked open-borders review was overseen by Home Secretary Theresa May as part of the Government's assessment of the balance of powers between the UK and Brussels.
Other proposals in the paper include giving British citizens a "national preference" by explicitly reserving jobs for them and limiting labour movement from poorer countries joining the EU to the UK until their GDP is 75% of Britain's.
Any attempt to challenge free movement rules would face resistance in Europe.