The firm also lowered its price target to $23 from $25 on shares of the Newton, MA-based senior living real estate investment trust.
The downgrade is primarily due to valuation.
"With the stock up 47% year-to-date (vs. 4% for the RMZ and 8% for the Healthcare REIT sector), we see limited upside given our view that SNH will have limited earnings growth in 2017," Jefferies wrote in an analyst note.
Current valuation suggests there is still some room for about 5% to 7% upside from current levels which is "decent," but not quite enough to merit a "buy" rating, according to the firm.
There is also risk of multiple compression in a rising rate environment over the next 12 months, Jefferies added.
Separately, TheStreet Ratings Team has a "Hold" rating with a score of C+ on the stock.
The company's strengths can be seen in multiple areas, such as its solid stock price performance, increase in net income and revenue growth.
But the team also finds weaknesses including disappointing return on equity, poor profit margins and weak operating cash flow.
Recently, TheStreet Ratings objectively rated this stock according to its "risk-adjusted" total return prospect over a 12-month investment horizon. Not based on the news in any given day, the rating may differ from Jim Cramer's view or that of this articles's author.
You can view the full analysis from the report here: SNH