U.K. government officials appear to be in favor of the deal, but problems could arise if the Labour Party opposes, the source said.
Pfizer disclosed earlier this week that it had twice approached AstraZeneca about a takeover, only to be rebuffed in both cases.
Pfizer and AstraZeneca declined to comment on the report.
Since Pfizer went public with its approach to AstraZeneca, investors and analysts have been expecting the largest U.S. drugmaker would come back with more than its initial offer worth $98.9 billion and increase the cash component. Under British takeover rules, Pfizer has until May 26 to announce its intent to make an offer for AstraZeneca, or walk away.
When AstraZeneca turned down the Pfizer offer, it did not simply say that the bid significantly undervalued the company; it put a "very" in front of it, noted John Boris, an analyst with SunTrust Robinson Humphrey.
"They're basically saying 'come back to me with a materially higher offer,"' Boris said. He predicted that Pfizer would raise the offer to about $110 billion, or $87 a share.
A purchase of AstraZeneca would not only bolster Pfizer's pipeline of cancer drugs in development but allow it to relocate its headquarters to Britain and take advantage of significantly lower tax rates there. It would also enable the company to use tens of billions of dollars it has overseas without having to pay high taxes for bringing the cash back to the United States.
—By Reuters with CNBC