The renewed discussions suggest that the two sides might be getting closer to striking a friendly deal, but there is no guarantee the talks will go anywhere, the Journal said, adding that the terms of the informal offer from Pfizer couldn't be learned.
Bloomberg reported earlier in the day that Pfizer may sweeten its offer for AstraZeneca to more than 63 billion pounds, or $106 billion, and raise the cash portion of the deal, to kickstart negotiations.
Citing people with knowledge of the matter, the Bloomberg report said a new bid may value AstraZeneca at more than 50 pounds ($84.47) per share and could come as early as next week.
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 Bloomberg 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 58.8 billion pounds ($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 Astra 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,'" said Boris. 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 redomicile in Britain to take advantage of significantly lower tax rates there, and 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.
Pfizer shares closed 0.4 percent lower at $31.15 on the New York Stock Exchange on Thursday.