The 21-year-old winger, who can also play as a central striker, has been training with the Ibrox side for the past week and admitted he’d jump at the chance to join Rangers permanently.
Dodoo made his debut in the Capital One Cup, grabbing a hat-trick against Bury and scoring again against West Ham United in the same competition.
He had a brief loan spell at Bury last season, playing five times.
Prior to training with Rangers, Dodoo said: “I used to watch them a lot when I was younger and obviously there’s the rivalry with Celtic.
“It’s a great club. Any player would be excited to play for a team like Rangers.”
Born in Ghana, Dodoo is eligible to play for England, and has one cap for England Under-18s, although Ghana are believed to be keen on the winger pledging his international future to the Black Stars.