It has also been a tough time for technology firms already on the public market. Shares in peer-to-peer lender Lending Club, for example, have halved this year on the New York Stock Exchange after it floated in December.
Square is classed as a “unicorn” – a Silicon Valley term for a start-up with a valuation greater than $1bn.
Uber is the unicorn with the biggest price tag, with its last funding round valuing it at $50bn. Reports suggest the mobile cab-booking app firm is sounding out investors over another fundraising round to the tune of $1bn.
Meanwhile, Airbnb raised $1.5bn in June in a deal reportedly valuing the home-rental service at $25.5bn.
Private start-ups have enjoyed a flood of investment in recent years from venture capital firms in California and from private investors hoping to grab a piece of the next Apple or Facebook.
But Canaccord Genuity analyst Bob Liao said traditional investors on Wall Street appear “increasingly sceptical” of the lofty price tags being placed on private companies.
“Public market rejection of high private market valuations has begun to impact private valuations,” he said.
Richard Holway, a veteran analyst at TechMarketView, said private funding of unicorns has gone into “crazy bubble territory”.
He said: “There is no value if we get into another bubble and in some areas we have got into another bubble. When we had the last bubble, it affected everybody.
“There are a lot of fairly valued companies that are making profits and generating cash and it would be wrong for our industry if they got sucked down because some unicorn gets overvalued.”