The Australian band was forced to halt its tour this month after lead singer Brian Johnson was told he risked total deafness if he continued to perform.
In a statement, the band said the rescheduled gigs would likely be staged with a guest vocalist.
A radio host in Atlanta, where AC/DC stopped its tour, said he had seen Rose in the city and that he was practicing with the band.
“It’s all but a done deal that Axl will front AC/DC for the 10 remaining shows” in the US, host Jason Bailey said on his show on rock station WNNX.
A representative for AC/DC did not deny the reports when contacted by NME.
“Nothing official to announce. Will update you if that changes,” they said.
The band is due to begin the European leg of its Rock Or Bust tour – which includes shows at London’s Olympic stadium and Etihad Stadium in Manchester – in Lisbon on 7 May.
The move, if confirmed, would come as a surprise, not least because Rose is currently preparing for a reunion with some of the original GNR members.
Rose will reunite for the first time since 1993 with Slash and Duff McKagan for the Coachella Festival in California and several other shows.
Johnson has reportedly voiced dismay at his swift departure from the band.
US comedian and radio host Jim Breuer said he had met the 68-year-old, who felt “kicked to the curb” by his bandmates as he believed his hearing issues were not as serious as stated.
Johnson joined AC/DC in 1980 after singer Bon Scott died following a night of heavy drinking in London.
His first album with the band, Back in Black, remains one of the top-selling albums of all time.
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