Jon and Mary Kaye Huntsman hinted Thursday night on Instagram that the former ambassador and governor is still toying with the idea of running a write-in campaign for Utah governor, despite having previously denied he would pursue one.

The Instagram post — which appears on the couple’s joint account — features a photo of Huntsman sitting next to his granddaughter, Isabel.

“Isabel trying to convince her Bapa to do a write in campaign for Utah Governor,” the caption reads. “He told her he’d think about it.”

Rumors have been flying for weeks about the possibility of a write-in bid by Huntsman, who lost the June 30 Republican gubernatorial primary to Lt. Gov. Spencer Cox. An informal group of Huntsman backers has publicly acknowledged they’re trying to convince him to compete with Cox and Democratic nominee Chris Peterson in November’s general election.

They note that the four GOP rivals split the primary vote so that no one candidate received majority support. Cox captured the nomination with 36% of the vote, while Huntsman finished in a close second with 35%.

“The primary process didn’t present what we believe will be the strongest candidate going forward,” said Alecia Williams, a spokesperson for the group that’s lobbying for a Huntsman write-in bid.

She has declined to identify the people who are involved in the effort.

When asked about a write-in bid last month, Huntsman told The Salt Lake Tribune he wasn’t interested.

“While we appreciate the continued enthusiasm from supporters throughout the state, especially after a very tight race, we won’t be pursuing any efforts for a write-in campaign,” he said in a prepared statement.

Huntsman daughter, Abby Huntsman, who worked on the campaign, replied to the original post Thursday night with the hashtag, “#allinhuntsmanwritein.”

But in response to a Tribune question about whether her father is seriously considering a write-in campaign, Abby Huntsman said Friday, “As we said last time, our family isn’t involved in any activity for a write in. Anything being done is from the outside.“

She continued, “[We] have been reached out to by many to do this. ... Support seems to be growing for the movement.”

State records also show that Huntsman’s mother, Karen Huntsman, has contributed $600,000 to his gubernatorial campaign since the primary election.

Utah Republican Party Chairman Derek Brown noted in a written statement Friday night that Huntsman has promised on several occasions since losing to Cox that he would “respect the will of the people” and was not interested in pursuing a write-in campaign.

“The party takes him at his word,” Brown said.

“The Utah Republican Party is 100% supportive of our party’s nominee, Spencer Cox, who won both the state convention and the primary election,” he continued. “In fact, Cox received almost 25,000 more votes in this year’s primary election than [Gov. Gary] Herbert received in the primary election four years ago. We are grateful that our candidates and the party are now unifying and focusing on winning this November.”

- Salt Lake Tribune reporter Taylor Stevens contributed to this report

Editor’s note: Jon Huntsman is a brother of Paul Huntsman, the chairman of The Salt Lake Tribune’s nonprofit board of directors.