TOM CRUISE is a three-time loser in marriage, but insiders say “Mad Men” star Elisabeth Moss is a perfect match!

A union between the “Mission: Impossible” hunk, 51, and 31-year-old Moss, who’s also a Scientologist, would likely please Church of Scientology officials. “Friends think it would be great for both of them – and Scientol­ogy,” said an insider.

According to the source, church leaders would probably “be delighted to have their lead­ing member become involved with another celebrity Scien­tologist.”

By all indications, Tom and Elisabeth – called Lizzie by friends – would make an ideal high-profile couple.

Lizzie is beautiful, smart and a little quirky,” said the in­sider. “She can hold her own in the spotlight, and marry­ing Tom would be good for both their careers. She has no children of her own and would be an ideal candidate to have one with Tom.”

The popular actress – who plays Peggy Olson on AMC’s 1960s hit advertising drama – was briefly married to former “Saturday Night Live” star Fred Armisen. But the couple split after just eight months in 2010, with Armisen admitting he was a terrible husband.

Meanwhile, Cruise has en­dured three failed marriages – to Mimi Rogers, Nicole Kid­man and Katie Holmes. Sources say he’s been lonely and is now ready for a self-assured, younger  described as “very mature.”

“Lizzie is on the verge of breaking out in Hollywood,” said a close source. “She would be a perfect complement to a superstar like Tom.”

And Tom is overdue for a new romance. He hasn’t had much luck since Katie Holmes shocked him with court papers in 2012 and asked for sole custody of their now- 7-year-old daughter Suri.

The actor was said to have briefly fallen for Jessica White, a gorgeous 29-year-old model and Scientolo­gist, although his reps denied it.

“Tom volunteered to be Jessica’s personal Scientology tutor, but nothing jelled between them,” said the close source. “Tom misses the companionship of a woman.”

As The ENQUIRER reported, the aging actor is sensitive about appearing over the hill and feels a younger woman would help him with younger audiences. Sources also told us that Tom even resorted to accompanying his 19-year-old deejay son Connor to clubs in a mostly futile effort to meet women.

But pals are optimistic that things could work out with Moss – espe­cially since she shares his beliefs.

Cruise admitted in court papers that ex-wife Katie filed for divorce at least in part so that Katie and Suri could leave Scientology, “but since Lizzie is a Scientologist, there would be no issues about raising a child in the church,” noted the insider.