If the two are elected, three of the company’s 14 board seats will be occupied by Ford family members. Currently there are two descendants of the founder on the board, Mr. Ford and his 72-year-old cousin,

Edsel Ford II,

who will retire from the board this spring, the company said.

Their appointments would extend a history of family oversight at the 118-year-old auto maker. Ms. Ford English’s 63-year-old father has served as executive chairman since 2006, and was chief executive officer and chairman before that.

Edsel Ford II, who is the father of Henry Ford III, has been a director since the late 1980s.

Elena Ford,

a great-great granddaughter of the founder, is Ford’s chief customer-experience officer.

In an interview, Bill Ford said the company’s family ties provide a long-term perspective that benefits shareholders and employees. He cited the 2008-09 financial crisis, when the company avoided bankruptcy by mortgaging most of its assets, including its blue Ford logo, while rivals

General Motors Co.

and Chrysler underwent government-led restructurings.

“The family involvement in the company has produced real and tangible results,” Mr. Ford said. “The family has been very willing to take short-term pain, like no dividends, to get us through tough times.”

The Ford family’s supervoting Class B shares give it 40% voting power and effective control over the company. Bill Ford has amassed a growing percentage of the Class B shares in recent years, totaling about 20% as of February 2020, according to regulatory filings.

Mr. Ford said he continues to add to his stake because he is confident in the company’s future. “All the different business opportunities that lay in front of us are really compelling,” he said.

Charles Elson,

a University of Delaware finance professor who specializes in corporate governance, said it would be unusual for three family members to serve on the board for a large public company, even one with a dual-class voting structure.

“It means more influence and more voice for the family, assuming those directors vote together,” Mr. Elson said.

Nell Minow, vice chair at advisory firm ValueEdge Advisors and a longtime advocate for shareholder rights, said adding two Ford employees to the board would run counter to the corporate trend of having a higher concentration of independent directors.

Ford shares have rallied since tumbling at the onset of the Covid-19 pandemic last year, when investors fled from the auto sector amid factory and supply-chain disruptions. Its stock price is up 52% this year and has more than tripled since March 2020. Shares rose about 4% Friday to close at $13.37.

Ford CEO

Jim Farley

took over in October, tasked with rejuvenating a company that has seen operating profit fall for five consecutive years. Mr. Farley has emphasized fixing Ford’s nagging quality problems and pushing further into offering digital services.

Mr. Ford said that the company’s 11 independent directors oversaw the vetting of the two younger Ford’s during the nomination process, and that he and Edsel Ford II weren’t involved.

He said the younger Fords provide a fresh perspective and knowledge of the company and the growth areas it is targeting. His daughter, for example, spent time as a manager in operations inside the company’s driverless car division, he said.

Ms. Ford English joined Ford in 2017 after working in fashion retailing, including a stint at

Gap Inc.

She has quickly ascended Ford’s ranks, now serving as a director in corporate strategy.

She is also a director at Rivian Automotive LLC, the electric-truck startup in which Ford has a minority stake and strategic partnership.

Henry Ford III has been at Ford for 15 years and is now a director in investor relations, after working in labor relations and as marketing manager for Ford’s performance-car division.

Write to Mike Colias at Mike.Colias@wsj.com