A source close to the LinkedIn said the company had decided not to pursue Monster after an assessment this week.
Monster shares closed up 19 percent at $9.33 on the New York Stock Exchange, giving it a market value of about $1.1 billion.
LinkedIn shares finished down 3.4 percent to $107.23 after Reuters reported on Friday afternoon that the social media company expressed interest in a potential deal for the Internet jobs-search company.
Monster, which runs Monster.com and HotJobs.com Websites, said in March it retained Stone Key Partners and Bank of America Merrill Lynch to review strategic alternatives, including selling all or part of the company.
New York-based Monster has since received expressions of interest from several strategic and financial buyers, the sources said. The company plans to send out financial information to the interested parties by the end of next week, they said.
The sources did not wish to be quoted by name because the process is private.
Representatives for Monster, LinkedIn and Silver Lake declined to comment. Stone Key Partners and Bank of America had no immediate comment.
The sale talks come as Monster's model of job ads is facing new competition from social media such as Facebook and LinkedIn, as well as several other rivals in an industry where the barriers to entry are low. The company said in January it would cut 7 percent of its staff, or 400 jobs.
Monster's 2012 share of online recruitment is estimated at 23 percent, below CareerBuilder.com's 32 percent, but ahead of LinkedIn's 16 percent. The online recruitment market is estimated at more than $5 billion.
Monster, which bought rival HotJobs.com in 2010, also competes with operators of specialized job sites, such as Dice Holdings Inc , which focuses on financial, IT and other sectors, and with hundreds of small operators.
Aggregators of listings, such as SimplyHired.com and Indeed.com, have also emerged as rivals.
Online jobs firms have also been buffeted by broader macro-economic challenges as have the traditional staffing companies such as ManpowerGroup Inc and Robert Half International Inc . The industry has seen a recovery in U.S. demand for workers, but softer staffing markets in Europe.
Monster has been fighting back with new technology initiatives, including Power Resume Search that makes it possible to identify workers with specific skills and BeKnown that allows employers to reach candidates via Facebook. That "app" could make it easier to find so-called passive job candidates who are currently employed.
SunTrust Robinson Humphrey analyst Tobey Sommer said recent U.S. job trends also make the company more attractive. The types of jobs being created in the current U.S. labor recovery play to Monster's strength in mid-level job categories, he said.
Monster would be a good fit for online professional networks such as LinkedIn or job boards such as CareerBuilder, BMO analyst Jeff Silber said in a research note on Friday.
"Given management's relatively open-ended comments, we believe there are a wide range of potential outcomes," he said.
For the latest tech news and reviews, follow Gadgets 360 on X, Facebook, WhatsApp, Threads and Google News. For the latest videos on gadgets and tech, subscribe to our YouTube channel. If you want to know everything about top influencers, follow our in-house Who'sThat360 on Instagram and YouTube.