The paper cited senior investment bankers and industry sources saying that informal conversations about a deal had taken place between the two but that no talks were currently under way after AstraZeneca resisted the approach.
Pfizer and AstraZeneca both declined to comment on the report to Reuters.
AstraZeneca, Britain's second-biggest pharmaceuticals group, has been frequently touted as a potential takeover target as it wrestles with patents expiring on a number of best-selling drugs, leaving future growth uncertain.
Despite these problems, the company has attracted attention for experimental cancer drugs it is developing, which could be interesting for Pfizer which has faced patent losses of its own, notably anti-cholesterol treatment Lipitor.
The two firms are familiar with each other's products working together on projects such as the pioneering of a new kind of clinical trial for cancer drugs announced last week.
Pfizer could use cash it has accumulated through overseas subsidiaries, which if repatriated to the U.S. would be heavily taxed.
In the past Swiss drug firm Novartis (NOVN.VX) and larger British peer GlaxoSmithKline (GSK.L) have been mentioned as potential suitors, although GSK has publicly said it is not interested in making a large acquisition in recent years.
AstraZeneca, which announces first quarter results on Thursday, has a market valuation of around $80 billion, compared with Pfizer - valued at $193 billion, according to Thomson Reuters data.
Earnings at AstraZeneca fell 6 percent in the fourth quarter of 2013, and the drugmaker has said it expects them to keep falling in 2014 as generic competition to Nexium, its popular heartburn and ulcer drug, takes a big bite out of U.S. profits from late May.
AstraZeneca has suffered a dry period in drug discovery in recent years and badly needs to find new medicines to replace blockbusters such as Nexium and Crestor, a treatment for high cholesterol that will lose patent protection in a few years.
Pfizer's last big acquisition was in 2009, when it bought U.S. rival Wyeth for $68 billion.
($1 = 0.5949 British Pounds)
(Reporting by Stephen Eisenhammer; additional reporting by Ben Hirschler; editing by Jane Baird and William Hardy)