A source familiar with the situation told Reuters at the weekend the two sides were in preliminary talks.
Buying Synthes would allow healthcare conglomerate J&J to further diversify its business, but a deal at $20 billion would be a premium of less than 9 percent to Synthes's market value on Friday, which some analysts said looked too low.
Shares in Synthes jumped 7 percent by 0740 GMT, after gaining 6.2 percent on Friday as talk circulated that J&J or Medtronic
In response to market speculation, Synthes Inc confirms that it is engaged in discussions with Johnson & Johnson about a potential business combination transaction, Synthes said in a statement.
Buying Synthes would be J&J's biggest acquisition and would help the cash-rich U.S. healthcare conglomerate further diversify its business by giving it a leading position in equipment to treat broken bones and trauma.
Synthes makes nails, screws and plates to fix broken bones as well as artificial spine discs.
CHAIRMAN IN DRIVING SEAT
Carla Baenziger, an analyst at Vontobel, said Synthes would double J&J's market share in spine work to about 30 percent, while in trauma it would be the clear market leader, with a share of around 57 percent, which could attract the attention of antitrust regulators.
Key to any deal will be Synthes Chairman Hansjoerg Wyss -- the second-richest person in Switzerland, with a net worth of $6.4 billion, according to Forbes -- who holds 40 percent of Synthes directly and another 8 percent through family trusts.
Given that big holding, an acquisition would need his buy-in, said ZKB analyst Sibylle Bischofberger, who is skeptical the deal will come off.
We would be surprised if Hansjoerg agreed to this as he is still putting his heart and soul into Synthes. But, because he is 75 years old, he is maybe prepared to talk with Johnson & Johnson in order to find a good succession plan, she said.
The medical device sector has been consolidating as pharmaceutical companies try to find other revenue streams to compensate for drugs going off patent.
Other recent medical device deals include the $5.8 billion acquisition of Beckman Coulter by Danaher Corp
There had previously been speculation that J&J, which had cash and short-term investments of $27.7 billion at the end of 2010 and will report results on April 19, was interested in buying British orthopedics company Smith & Nephew
Shares in Smith & Nephew, which has a market value of around $10 billion, fell 4 percent.
Medical devices and diagnostics accounted for 40 percent of J&J's $61.6 billion in 2010 sales, but the business has been hit by competition and recalls in its hip and knee replacement unit.
J&J owns around 250 separate companies under its corporate umbrella. The group attempted to buy U.S. medical device maker Guidant several years ago, but was outbid by Boston Scientific Corp
The healthcare sector has seen a string of international mergers as big companies seek to plug gaps in their businesses, including the recent acquisition of U.S. biotech company Genzyme by France's Sanofi Aventis
Canada's Valeant Pharmaceuticals International
(Editing by Will Waterman and Ben Hirschler)