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.