Rak-Su star Stephenson reportedly claimed to Jossa that Osborne cheated on her with Stephenson’s ex-girlfriend Gabby Allen.
The Sun reported that Jossa threatened to quit the show and was allowed by bosses to leave Osborne a voice message about Stephenson’s claims.
ITV declined to comment on the matter.
Former The Only Way Is Essex star Osborne touched down in Australia on Wednesday and immediately dismissed the idea he is set to confront Stephenson.
He told The Sun: “I’ve got nothing to say to him, only my wife.
“I’ve got nothing to worry about. I’m just coming down here to support her and that’s the only reason I’m here.
“I’m just excited to see her so the last person on my mind is Myles.”
Osborne, 28, arrived Down Under with his and Jossa’s children Ella, Mia and Teddy, and shared a picture from the airport on Instagram.
He wrote: “Just landed in Oz! I seriously can’t wait to see their little faces when they see mummy.
“Obviously Mia hasn’t got a clue bless her!
“Keep smashing it @jacjossa. We are here waiting for you when you get out.”
Osborne has previously said he does not expect his wife to leave the jungle any time soon.
He said in a video on his Instagram story: “I think she will get to the final at least. I think she should win it, that’s my opinion, I might be a little bit biased.
“She will be at the final, so it’s going to be a little while.”
Jossa and Osborne first began dating in 2014 and got engaged a year later.
They married in 2017 but have faced rocky times after Osborne was faced with allegations of cheating on Jacqueline with Gabby and fellow Love Islander, Alexandra Cane.
He, Gabby and Alexandra have denied the claims.