Stryker's shares tumbled more than 4 percent, and Boston Scientific's rose nearly 8 percent Monday in afternoon trading. They were halted before Boston released its statement.
"Boston Scientific ... is aware of reports speculating that the company has been approached by Stryker Corporation regarding a potential acquisition." the company said in a filing with the Securities and Exchange Commission. "Consistent with its practice, the Company does not comment on market rumors or speculation."
A deal would unites two medical device giants into a powerhouse with a combined value of more than $110 billion, The Wall Street Journal reported, citing people familiar with the matter. Sources told the publication it was unclear whether Boston Scientific is receptive to the offer.
Boston Scientific has a market capitalization of $47.6 billion. Its stock has risen 38 percent this year and was on pace for its best daily performance since January 9, when it gained 8.3 percent.
Stryker, with a market capitalization of $64.9 billion, has seen its shares gain about 13 percent his year. They dipped nearly more than 3 percent Monday, on pace for their worst day since April 6.
A Stryker spokesman said as a matter of company policy, Stryker does not comment on potential mergers and acquisitions. A Boston Scientific spokeswoman told CNBC ahead of the the company's official statement that it does not comment on rumors or speculation.
A combined company would offer a broad range of medical devices. Stryker's lineup includes orthopedic products, such as parts for knee and hip replacements, while Boston Scientific's portfolio includes cardiac products like pacemakers.
There's some overlap between the two companies' offerings, including spinal cord stimulators, which are implantable devices used to treat chronic pain.
A deal could allow the two companies to better compete with Medtronic, a medical device behemoth with a market value of $117.3 billion. The company's shares fell 0.4 percent Monday.
BMO Capital Markets analyst Joanne Wuensch said if Stryker and Boston Scientific were to combine, it would be one of the final "major puzzle piece" acquisitions within the greater medical technology industry consolidations. In a note to clients, she cited other recent deals, including Abbott's acquisition of St. Jude Medical last year.
Yet J.P. Morgan analyst Robbie Marcus said he and his team "aren't big believers" in the bigger is better strategy. His questions, he wrote Monday in a note, include whether a deal is financially possible, why Stryker would want to take on the risk when they've been executing so well, whether Boston would willingly sell, and whether there are any other potential bidders that could enter the mix.