The private equity firm that agreed to fork over nearly $10 billion to scoop up Subway faces stiff challenges to revive the troubled brand amid plummeting foot traffic, according to an industry expert.

The family-owned sandwich maker — which accepted a $9.6 billion offer from Roark Capital last week — has seen overall foot traffic at its US franchises plunge 21.6% offer the past four years, according to exclusive data from Placer.ai shared with The Post.

Subway’s dropoff comes as rival Jersey Mikes has seen an increase of 39.1% over the same period from May 2019 to May 2023, the data showed.

The trend doesn’t bode well for Subway’s new owner, according to Andrew Pudzer — the former CEO of CKE Restaurants, whose fast-food brands include Carl’s Jr. and Hardee’s.

You never want to see traffic down significantly, said Pudzer, who helped sell CKE to Roark in 2013 and stayed on as the company’s chief executive until 2017.

If you are going to build your business you cant continue to lose traffic at a significant rate.

Two other two sizable sub chains, Jimmy John’s and Firehouse Subs, also lost traffic during that period but at much lower rates than Subway, according to the data. Jimmy Johns was down 8.8% and Firehouse Subs sank 13.2%.

Subway’s foot traffic began to inch up in the past year, rising .08% from May 1, 2022 to May 1, 2023, but was still well off gains made by Jersey Mikes (13.7%) and Jimmy Johns (2.4%) over that span, according to Placer.ai.

Firehouse Subs was down 4.2% during that period.

Subway, one of the nation’s largest fast food chains with more than 20,000 franchises in the US, touted its positive same-store sales this year, which was up 9.3% in North America compared to the prior year.

We are pleased with the continued progress of our transformation journey, which has refreshed our ingredients, improved our menu, helped boost our franchisees profitability and resulted in 10 consecutive quarters of positive sales, a Subway spokeswoman told The Post on Monday.

Roark Capital — an Atlanta-based private equity firm and backer of restaurant conglomerate Inspire Brands — last week agreed to buy Subway for $9 billion plus $600 million more if Subway hits certain performance targets. The deal still must clear anti-trust regulators.

Pudzer expects Roark to dive into rebranding the troubled chain’s “Eat Fresh” slogan.

When Roark bought Arbys in 2011 from Nelson Peltz it was in serious trouble and a chain few wanted to frequent, Pudzer noted.

The Roark team came up with great new products and the now-ubiquitous ad campaign, We Got the Meats.

Subway needs a new slogan, Pudzer said.

The chain has suffered several public relations nightmares over the past decade — beginning with the conviction of spokesman Jared Fogle for possessing child pornography in 2015.

More recently, it was hit with allegations of selling fake tuna and chicken, and suffered backlash over having soccer star Megan Rapinoe promote the brand and then kneeling during the national anthem.

I think for many years Subway had great success because their target market felt good about going there, Pudzer told The Post.

Theyve kind of lost touch with their target market. People feel its not a place for them anymore. They need to figure out how to make their customer comfortable to be there.