The capital injection of between 4 and 5 billion euros in the lender is set to be approved on Monday by the national bank rescue fund FROB, the source added.
It follows weeks of wrangling behind closed doors between Madrid and the European authorities on the need for help for the lender, heavily exposed to soured real estate assets.
A spokesman for Bankia declined to comment.
Bankia reported on Friday losses of over 4 billion euros in the first of half of 2012, while its core capital ratio -- a measure of financial strength -- was 6.3 per cent.
Its parent company BFA had a capital ratio of 1.8 percent, far below the 9 percent level the government requires lenders to meet at the end of the year under the terms of the 100 billion-euro European aid for Spanish banks.
FROB has 4.14 billion euros available, according to the economy ministry.
Banking sources told Reuters that FROB could inject cash into Bankia or use state-back debt instruments to capitalise the bank, which it could in turn use as a collateral to obtain cash from the European Central Bank.
That constitutes an advance on the 19 billion euros that Bankia asked the state to inject as part of a total rescue package of 23.5 billion euros.
Several senior sources told Reuters last month that the euro zone wanted to wait for the conclusion of a final stress test of Spain's wobbly banking sector to be published in the second half of September before disbursing the first tranches of the aid.
In June, consultancy firm Oliver Wyman said Spain's banks would need as much as 62 billion euros of extra capital from funds to be made available under a European rescue package.
Shares in Bankia were 2.2 percent lower at 1.394 euros at 1039 GMT after temporarily paring losses when Spain's Economy minister Luis de Guindos said on Onda Cero radio that the FROB board would approve the decision to inject capital "in the next hours".
De Guindos also said Spain remained committed to meeting its EU-agreed deficit target of 6.3 percent of its gross domestic product in 2012 despite bad data for the first seven months of the year.
"We have to go from a public deficit of 9 percent last year to 6.3 percent this year, a reduction of almost three percentage points in a recession environment," he said.
Spain reported a deficit of 8.9 percent of GDP last year, but has recently revised down economic growth for last year, which might have bumped the deficit figure up a little.