The sacked Sunderland and ex-England winger was jailed last month after he was convicted of sexual activity with a 15-year-old following a trial at Bradford Crown Court.
Johnson had already admitted grooming the girl and a separate, less serious charge of sexual activity with her.
Johnson will be soon be moved from Armley Prison in West Yorkshire to a jail closer to his native North East, according to reports.
The Prison Service refused to comment on newspaper reports that he will be sent to Holme House jail on Teesside, HMP Durham or the maximum security jail at Frankland just outside the city, which is home to notorious child killers like Ian Huntley.
A Prison Service spokesman said: “We don’t comment on individual prisoners.”
Holme House in Stockton is just 14 miles down the A19 from Johnson’s £1.5 million home in the village of Castle Eden, where until his trial he lived with Stacey Flounders and their baby daughter.
An official at Bradford Crown Court confirmed Johnson’s legal team has lodged an appeal against sentence.
The 28-year-old former Middlesbrough and Manchester City attacker has already begun an appeal against his conviction for the one offence for which he was found guilty.
On the Adam Johnson’s Appeal Fight page on Facebook, run by his sister Faye, a post said: “Adam’s appeal against his sentence has now been lodged!”
“Thanks everyone for your support it means a lot! X”
The appeal page has been “liked” by more than 8,000 people.
Passing sentence last month, Judge Jonathan Rose said Johnson had caused his victim “severe psychological harm”.