Anna Eberstein, who Grant is rumoured to have been romantically linked with, has given birth, but the 55-year-old actor has not yet confirmed whether he is the father.
The Swedish newspaper reported that Eberstein's baby baby "saw the light of day for the first time" on 16 December.
Rumours arose in October 2015 that Eberstein was pregnant for the second time. The news was revealed by American entertainment site, ET, who state that Grant and Eberstein already have a three-year-old son called John.
Grant has two other children, Felix, two, and Tabitha, four, with former partner Tinglan Hong.
Grant's ex, Liz Hurley, stated that Eberstein was carrying Grant's baby on American TV show Watch What Happens.
Answering a question about Grant welcoming his fourth child, she said according to the Mail: "Yeah it is surprising. But he is a good daddy, very good."
HuffPost UK Parents has contacted Hugh Grant's rep for comment about the birth.
Liz Hurley and Hugh Grant at the Four Weddings premiere in 1994 - is this what they call a defining moment? Safety pins and Versace was all it took. (credit:PA)
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Another premiere (Notting Hill), another Versace dress for Liz and Hugh - 1999 (credit:PA)
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In style at the Annual Fashion Awards - 1999 (credit:PA)
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Hugh Grant with Jemima Khan in 2007 (credit:PA)
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Keeping up with the Hurleys - Jemima Khan with Hugh Grant at the premiere of Music and Lyrics in 2007 (credit:PA)
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Hugh Grant and Liz Hurley - just an unassuming, modern British couple - at the Cannes Film Festival, 1996. (credit:PA)
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Hugh Grant and Liz Hurley at the Diamonds Are Forever Gala in 1999. (credit:PA)
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Hugh Grant and Liz Hurley - dear me, they went to a lot of premieres. This time it's Mickey Blue Eyes, 1999. (credit:PA)
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Hugh Grant and Jemima Khan - a rare PDA from the notoriously camera-shy Grant. The couple were at Sir David's Frost summer party in 2006. (credit:PA)
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Hugh Grant and Jemima Khan in 2006. (credit:PA)
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Keeping it in the family - Liz Hurley and then-husband Arun Nayar attend Hugh Grant's 48th birthday party. Jemima Khan was also a guest. (credit:PA)