The rapper appeared to address infidelity on his part during their marriage in his new song "Hurricane"

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Kim Kardashian and Kanye West attend the 2020 Vanity Fair Oscar Party hosted by Radhika Jones at Wallis Annenberg Center for the Performing Arts on February 09, 2020 in Beverly Hills, California.
Kim Kardashian West and Kanye West
| Credit: Frazer Harrison/Getty

Kanye West appears to be well aware of mistakes he made in his marriage to Kim Kardashian West.

The rapper, 44, seemed to suggest he'd been unfaithful in the lyrics to his new song "Hurricane"  — and, according to a source close to him, he feels remorseful about the pain caused his estranged wife.

"There were things that happened in their marriage that Kanye regrets. He wasn't always the best husband," the source tells PEOPLE. "He knows that he hurt Kim. He will always love her though."

The Keeping Up with the Kardashians alum, 40, filed for divorce from West in February after nearly six years of marriage and four children: daughters North, 8, and Chicago, 3½, and sons Saint, 5½, and Psalm, 2.

RELATED VIDEO: Kanye West Seems to Hint at Cheating on Kim Kardashian 'After 2 Kids' in New Song 'Hurricane'

Though an insider told PEOPLE last week that Kardashian West has no plans to call off the split despite a slew of public appearances in support of West's new album Donda, the source says that West still wears his wedding ring "occasionally."

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"Sometimes it seems that he hopes Kim will change her mind about the divorce," the source says.

Reps for West and Kardashian West did not immediately return PEOPLE's request for comment.

In the lyrics of "Hurricane," the fifth track off Donda, West appeared to hint at infidelities after North and Saint were born.

Kim Kardashian and Kanye West attend the Balenciaga show as part of the Paris Fashion Week Womenswear Fall/Winter 2020/2021 on March 01, 2020 in Paris, France.
Credit: Pierre Suu/Getty

"Here I go actin' too rich / Here I go with a new chick / And I know what the truth is / Still playin' after two kids / It's a lot to digest when your life always movin'," he raps on the track.

He also appeared to reference the couple's California mansion, which was featured last year in an issue of Architectural Digest, rapping: "Architectural Digest, but I needed home improvement / Sixty-million-dollar home, never went home to it / Genius gone clueless, it's a whole lot to risk."

A separate source previously told PEOPLE that the lyrics were "in a way [Kanye's] testimony of everything he did wrong and his apology and taking accountability."

Another track, "Lord I Need You," seemed to allude to the fact that Kardashian West brought their four children to his Donda listening parties.

Kim Kardashian Shares Photos from Controversial Donda Listening Experience
Kanye West "Donda" listening experience
| Credit: Kim Kardashian/Instagram

"Time and space is a luxury / But you came here to show that you're still in love with me," West raps on the song.

A source told PEOPLE last week that while filing for divorce from West "was always the most difficult decision" for the SKIMS founder, the couple "had issues that they couldn't solve."

"She will always love Kanye though," the source said. "It's taken them months to get to this point. Kim is happy that they get along and that things are amicable."