A handful of interested parties have been invited to make second- round offers, with a mix of trade and private equity bidders at the table.
SMG has appointed corporate finance company Hawkpoint to oversee the auction process and it is thought that "final offers are imminent".
Media Week understands that a leveraged management buyout, first mooted several months ago, is still one of the options.
One industry insider said the sale of Primesight had been brought forward after SMG bosses decided there was no reason why it could not be on the market at the same time as Virgin Radio, which SMG is expected to float on the stock market. A Virgin outcome is expected by the end of September.
SMG is also looking to sell its cinema advertising arm, Pearl & Dean.
The company, which owns STV in Scotland and Ginger Productions, aims to achieve £2.5m in cost savings this year by selling the three firms and restructuring its TV arm.
Rob Woodward, chief executive of SMG, said in July: "We have had a thorough look at the business and taken some short-term remedial actions to deliver sustainable growth."
Primesight was first put up for sale earlier this year, but new management at SMG removed it from the market in April in the belief that it could get a higher price.
Clear Channel, parent of rival outdoor company Clear Channel UK, had some of its assets on the market at the time, which could have distracted potential buyers from Primesight.
SMG was originally seeking £90m for Primesight, which owns the rights to 13,500 six-sheet panels and 141 large format backlit panels, but analysts valued it at nearer £55m, although this has now been revised to around £60m.
Since then, revenues at the outdoor company have increased by 8% and parent company SMG is trading in line with expectations, it announced at its annual general meeting in May.
SMG and Primesight declined to comment.