The 16-year-old forward is one of the most promising youngsters north of the border and had tests at Liverpool and Manchester United last year.
The Daily Record reports that the Rangers have agreed to fees with the County of Scottish Championship, but have not yet reached a personal settlement with Graham.
The Rangers are reported to be “facing a fight” to complete the transfer amidst the interest of the Wolves and Leeds United championship leaders.
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Graham only joined the county last year, but had an amazing shape for the under 16 and under 18 club.
Meanwhile, former Wolves side back Barry Douglas is slated to make their way to Ibrox in the next transfer window.
Douglas was controversially allowed to join Leeds two years ago after playing a key role in promoting Wolves in the Premier League.
He had 14 assists and five goals as the Nuno Espirito Santo team won the title.
But the 30-year-old failed to recreate this kind of form at Elland Road and did not play for Marcelo Bielsa’s team in the two months before the suspension of football.
“Bielsa has been consistent with his team selection and it will only become more difficult if they go up,” former West Brom forward Kevin Phillips told Football Insider.
“The signatures will arrive and move the players who are already in the camp, so it would be very difficult for him to break into a Leeds club in the Premier League. If they go up, many other players will be in the same situation.
“It would be a great opportunity to go to a club like the Rangers. It will be a very attractive proposition for the player and I can see it happen. “