Hasbro Inc. HAS -0.62% has made a takeover offer for rival Mattel Inc., MAT -1.69% according to people familiar with the matter, a potential combination that would unite the two biggest U.S. toy makers and put Barbie and G.I. Joe under the same roof.

Hasbro’s approach to Mattel was made recently, one of the people said. The terms of any possible deal couldn’t be learned, and the approach may go nowhere.

After taking a beating this year, Mattel’s market value stands at about $5 billion, or less than half as much as Hasbro’s, which is currently more than $11 billion. Hasbro, which is based in Pawtucket, R.I., comprises brands including Nerf, Transformers and My Little Pony. The company has made a push into getting the rights to television and movie franchises such as Disney’s “Frozen” and “Star Wars,” and its results have outperformed those of Mattel.

Mattel, based in El Segundo, Calif., is the maker of Barbie dolls, American Girl dolls, Fisher-Price and Hot Wheels toys. The company has been struggling with losses and weak sales, forcing it to suspend its dividend and outline plans to slash costs and scale back new product launches. It hired a new chief executive, Margo Georgiadis, from Google earlier in the year after a previous turnaround effort stalled.

Representatives for both companies declined to comment.

Shares of Mattel have fallen 47% this year, ending Friday’s session at $14.62 after gaining 5% on the day. Hasbro, meanwhile, has gained 18% on the year and closed Friday at $91.45, up 3.1% on the day.

The possibility of a tie-up between the companies has long been discussed by analysts and investors as the toy industry has come under pressure from customers moving a higher share of their spending to technology-based items. Indeed, this isn’t the first time the companies have discussed a union, people familiar with the negotiations have said.

Some analysts have long been skeptical about a deal between the two toy giants, however, in part because they question whether antitrust regulators would approve a combination of the industry’s two biggest players. Hasbro has jettisoned all of its manufacturing operations in recent years and buying Mattel would put it back into the business of owning toy factories.

What’s more, the two companies also have headquarters on opposite sides of the country and analysts believe melding their two vastly different cultures could prove problematic.

It isn’t clear how receptive Mattel would be to a deal. Its stock is less than a third of where it was a few years ago and officials of the company may be wary of selling at such a depressed price.

Hasbro has held up relatively well. Chief Executive Brian Goldner has forged close ties to Hollywood, where the company is producing movies and is a favored partner for creating toys tied to films. In recent years, Hasbro won the coveted license for Walt Disney Co.’s Disney Princess characters and has long made toys tied to the media company’s “Star Wars” franchise.

Hasbro is also more advanced in telling stories and creating content around its large brands, including a string of feature-length films for its Transformers franchise and more-recent launches like a My Little Pony movie.

After years of trailing behind Mattel, Hasbro passed its rival in quarterly revenue for the first time since 2000 in April, highlighting the diverging fortunes of the two toy makers. Last month, Hasbro reported a 7% increase in third-quarter sales, while Mattel reported that sales dropped 13% in the quarter.

In September, pressure on toy makers ratcheted up further when retailer Toys “R” Us filed for chapter 11 bankruptcy protection, undone by a hefty debt load and the rapid shift to online shopping. That same month, Lego AS said it would cut 8% of its global staff.

Both Hasbro and Mattel were stung by the Toys “R” Us bankruptcy, which threw a major sales channel into turmoil and prompted them to stall deliveries to the retailer, but Mattel’s problems run deeper. The new regime laid out a plan that would keep the company in turnaround mode for a few more years as it tries to fix problems that it blamed on past management. Those included a proliferation of new toys with little staying power that heaped additional costs and complexity onto Mattel’s supply network.

Mattel executives have said that past cost-cutting programs were largely ineffective. The company is seeking to cut another $650 million in annual costs.

Over the years, both companies have considered some sort of combination.

Mattel has often analyzed possibly buying Hasbro and executives were confident that regulatory concerns could be overcome, given that the two companies wouldn’t have too dominant a share in the industry, said a person familiar with the matter. A bigger concern was that a tie-up could trigger change-of-control clauses in the numerous licensing agreements with the likes of Disney, Nickelodeon and others.

During previous discussions, including one in the past two years, Mattel executives ultimately decided they could boost the company’s stock price themselves in a highly cyclical industry where a hit toy line can quickly improve fortunes, this person said.

Write to Dana Mattioli at dana.mattioli@wsj.com and Paul Ziobro at Paul.Ziobro@wsj.com