The Scotland captain and Parkhead midfielder are close after spending years together at Liverpool, winning the Premier League together in 2020.
Oxlade-Chamberlain joined Celtic as a free agent last month and Robertson's contract at the English giants expires this summer.
As a boyhood fan of the Parkhead club there have been suggestions of a romantic return to the club where he was in the academy. His pal would love to see it happen.
Oxlade-Chamberlain told the Celtic Podcast: “We’re very close with Robbo and his family, his mum and dad. We were next door neighbours for years and years.
“I knew all about Celtic and Glasgow from them for years. Robbo makes no secret of what he thinks about this club so when I was linked he was the first one to call me and said get yourself up there now.
“I’m obviously really close with Robbo and his missus and the kids and my missus is really close with them also. We get on really well with them. So having him as a reference point was perfect for me.
“He told me where I need to live, where I need to go, he’s told me everything. He’s a proper Glasgow boy.
“I just said to him ‘it’s a shame you’re not here with me.’ He might join me soon, he’s a bit younger than me, Robbo. I’d hope to see him here one day. I think he’d be amazing.”