Initial reaction to the report sent shares up sharply before being halted about 7% higher to around US$34.
According to the Journal story, which is attributed to anonymous sources, it is unclear whether Boston Scientific is receptive to the approach.
The Marlborough, Massachusetts, company has a market cap of about US$47bn, while Stryker is valued at US$64bm.
After trading in Boston Scientific resumed, shares leapt 10% to US$ 35.12, while Stryker shares dipped 3.6% to US$172.50 in midday trading.
-- Updates share prices --