Independent audit reports based on Spanish economy's troubles last month calculated the country needs more than $76 billion to stave off collapse of its banking system.
Analysts say the estimate may be out of date and a larger cash injection may be necessary.
A bailout will involve interventionist monitoring of finances by the European Commission, European Central Bank and the International Monetary and may force Rajoy to make deeper cuts than those in a highly unpopular austerity package already seen as the cause of rioting and civil strife in the country.
Spain's once vibrant economy was brought to its knees by speculative property deals that went sour in the aftermath of the 2008 global economic crisis. Deprivation is so widespread that analysts see Spanish society edging toward an explosive state that threatens Rajoy's administration and the country's stability.
Spanish Economy Minister Luis de Guindos, in a London address, insisted the government wouldn't request a bailout but critics said a distress call from Madrid for access to the eurozone rescue funds could come over the weekend.
Spanish officials dismiss suggestions that a bailout plea is imminent.
Protesters interrupted the minister's speech at the London School of Economics with placards that read "Spain for sale."
Opposition to austerity cuts initiated by Rajoy has drawn together erstwhile political rivals but analysts say the prime minister's $17 billion proposed cuts in all economic sectors may not be implemented while the Spanish banks' financial condition deteriorates.
The austerity package also assumed the country's regions will obey Rajoy, which seems increasingly unlikely.
Amid the protests, de Guindos declared, "Spain does not need a bailout at all" and repeated his government's assertion its policies will benefit not only Spain but the rest of the 17-nation eurozone in the 27-member European Union. He said the government is confident of bringing in investors to help rescue the banks.
Britain isn't in the eurozone but its financial services sector is feeling the heat from the continuing crisis in the European Union's financial heartland.
Spain's growing unemployment, currently 25 percent and said to be growing, is also worrying neighboring states who fear an influx of Spanish job-seekers.
Spain is the fourth eurozone country to face a bailout after Greece, Ireland and Portugal received funds to prop up their financial systems, but not before submitting to Brussels conditions for heavy cuts in expenditure, higher taxes and other changes seen as hits on their sovereignty.
Spanish politicians say Spain's size may protect it from similar humiliating terms for EU cash because Spain's economy is double the size of the other three recipient countries put together.
However, analysts warn that Spanish vulnerability is likely to increase as Madrid continues to postpone a bailout call. The bailout of the other three countries has renewed questions about its effectiveness.
Critics say some of the bailout terms are far too cumbersome and intrusive. Frequent inspections of sovereign accounts by the European Commission, IMF and ECB is one of the conditions likely to prove to be a headache in Spain, which has regions still operating independent of Madrid despite Rajoy's repeated attempts to bring their finances into line.