The corporate and financial comms specialist is understood to have been seeking around £20m ($26m) for the 51 per cent stake owned by private equity firm Vitruvian since 2011.
A sale would include debt liabilities.
The process to sell Vitruvian's stake began last Autumn and it is understood discussions have taken place with a small number of private equity companies.
'Paused not stopped'
Tim Linacre, senior managing partner, corporate and capital markets, at Instinctif told PRWeek: "That process has been paused rather than stopped.
"A transaction would only happen if it's in everyone’s interests for it to occur, and this process has been going on a bit long. We thought, with summer coming up, let's pause it, concentrate on the day job.
"We can re-look at some point in the future about bringing on board a new investor in what we hope will be a slightly faster process."
The company in its entirety was valued at around £45m when Vitruvian invested seven years ago. At that time the business, then known as College Hill, employed more than 300 people in 13 owned offices in Europe, Africa, Asia and the US, with annual turnover of £40m.
Instinctif generated global revenue of $50.1m (£37.8m) in 2017, a rise of five per cent on the previous year, according to PRWeek’s Agency Business Report. Headcount was not disclosed.
Some industry sources have said slow growth in recent years and tightened margins may have deterred potential investors.
However, an Instinctif source said the group remains profitable, generating roughly £5m to £6m in profit annually with growth of around seven per cent, and highlighted factors such as uncertainty over Brexit.
Linacre said Instinctif was in a "position of strength" regarding the sales process, describing the company as "a profitable business generating cash".
He also said Vitruvian was "not in a rush" to sell.
The 49 per cent of the business not owned by Vitruvian is shared fairly evenly across a number of employees, including CEO Richard Nichols.
Instinctif was the Gold winner in the Large Agency of the Year category at this year’s PRWeek UK Best Places to Work Awards. It was also named International Agency of the Year at the recent PRWeek Global Awards.