Pregnant Chelsea Clinton is fulfilling Bill and Hillary’s cherished dream of becoming grandparents, and her husband – who’s been blatantly snubbed by Bill for years – may finally be accepted into the family, say insiders.

Bill has repeatedly given the cold shoulder to Chelsea’s husband Marc Mezvinsky, but now it appears the conflict is winding down – all thanks to the baby!

“Marc is scoring points with Bill because of Chelsea’s pregnancy,” declared a close source. “Bill is delighted that he and Hillary are finally becoming grandparents, and this is allowing Marc to work his way into the so-called ‘circle of trust.’

But he’s clearly not there yet. With the Clintons, image is everything. And it was clear where Marc ranks when Chelsea recently an­nounced her pregnancy at a New York City event for the Clinton Foundation. While Hillary was seated next to her, Marc was in the back of the room.

“Still, this is a good start for him in terms of rehabilitating his image in the eyes of his father-in-law.”

In July 2010, Chelsea, now 34, tied the knot with the investment banker – but it didn’t take long for him to find himself in the Clinton doghouse!

The ENQUIRER revealed that Bill was fum­ing when Marc quit his Wall Street job just six months after the wedding so he could “sort his head out.” Incredibly, Marc lived the life of a ski bum in Wyoming for a while, leaving Bill’s only child to fend for herself in New York.

After that, Marc was treated “like a second-class citizen,” said the close source.

He even suffered the indignity of being seated behind the rest of the family – includ­ing his bride Chelsea – at Bill’s 65th birthday celebration in the famed Hollywood Bowl.

Insiders reveal that last summer, the 36-year-old – now back in investment banking – was not invited to spend time with the Clintons when they rented an $11 million estate in Sagaponack, N.Y. Chelsea was in England, but Marc was kept away while the family en­tertained guests, including Bill’s hell-raising brother Roger.

The ENQUIRER also reported that Marc was left out of a star-studded trip to Af­rica for one of Bill’s passionate causes, rais­ing awareness of that continent’s rampant poverty. Chelsea went without her husband.

But now the ice between Bill and his son-in-law is beginning to melt, say sources.

Hillary was recently spotted talking at length with Marc at a premiere party for “Of Many,” a film that Chelsea helped produce.

Meanwhile, the politically savvy Clintons are expected to make the most of Chelsea’s baby – due this fall – during Hillary’s likely run for the White House in 2016.

“The image of Bill holding his grandchild will soften the memories of his old ‘bimbo erup­tions,’ which the Republicans will raise,” said the source.

“And if Marc plays his cards right, he may earn a bigger role in the family as his mother-in-law campaigns for the presidency.”