The 19-year-old has made six senior appearances for the Magpies, most recently turning out against Newcastle United’s Under 21s in the EFL Trophy.
“I came in the morning after the Newcastle game and Mark Crossley told me Paul (Hart) wanted to speak to me,” Osborne told the official website.
“He told me there and then – he said I’d been doing really well and that I deserved it.
“Now I just want to carry on being in and around the first team and push for a spot. I’ll be training hard every day and looking to show what I can do week in, week out with the Under 23s."
Osborne, who joined Notts from Dunkirk Colts, added: “As a winger, I love getting at players and trying to create for the team.”
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