Boyd, 26, will leave Ibrox when his contract expires this summer and has been linked with moves to Turkish club Kayserispor, Birmingham, Blackburn, Newcastle, Middlesbrough and Wolves.
Speaking publicly for the first time since his departure was confirmed last week, Boyd revealed he has yet to decide where his future lies.
But after winning back-to-back Scottish Premier League titles and becoming the SPL's all-time leading goalscorer, he believes it is time to move on.
He told the Scottish Sun: "This has been the biggest decision of my life. I've spent months thinking about what to do and still haven't come to a final decision.
"But it's time to leave Scottish football. I need a fresh challenge."
A report last week linked Boyd with what would be a sensational move to Celtic, but the Parkhead club categorically denied any plans to sign the Scotland striker.
Boyd added: "Right now I'm considering my future and have a lot to think about in the coming days. I know there's been talk of me going from Rangers to Celtic. But, if I did that, it wouldn't be the penalty box I'd be in, it would be a wooden box!
"I'll sit down with my family over the next few days and come to a decision. But swapping Ibrox for Parkhead will not be happening."
Boyd pleaded for understanding from Rangers fans, insisting he would have already made a lucrative switch to Turkey if money was the motivating factor.
He added: "I've won everything I hoped to win at Rangers. I've been the top goalscorer at the club every season since I arrived from Kilmarnock. It's now time to move on.
"I could've stayed but is it really going to get any better? That's what I've been asking myself. Back-to-back titles is a tremendous achievement for everyone at the club and I was part of that. I just like the idea of leaving on a high."