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The 16-year-old attacking midfielder has been linked with both halves of the Old Firm amid the possibility of Arsenal allowing him to leave temporarily in search of regular senior football.
Former Aberdeen chief executive Keith Wyness, speaking to Football Insider's Inside Track podcast, believes Rangers would currently represent the better option for Dowman and claims the situation at Celtic could count against them.
Wyness said: "I think for Dowman, it would be coming into a club that has got stability, which is what Arsenal will want for him, to be sure he's going to get minutes, which Rangers proved they can do with Mikey Moore."
He continued: "He would be part of a whole stable organisation that's moving forward, which Rangers, as I just said, seem to be showing signs of.
"Celtic at the moment would be the complete opposite of that. To me, there's only one winner in this case if it is in fact a Scottish loan. Although I think maybe the Championship might be better for him if he were to go anywhere.
"But if it was to be Scotland, then Rangers would be the best option. I think it would be excellent for all parties. But for Dowman, I think that at his age, it's a long way to go to Glasgow, and you're in a big inferno in Glasgow.
"I know Moore managed it, but I think some of his family were up there as well at the same time. So it's a difficult one, but a lot of factors to consider.
"But on the football side, I think Rangers are the clear winners."