Despite being highly-regarded at the Riverside Stadium, Spence was allowed to link up with Nottingham Forest on a season-long loan deal in the summer.
During his time at the City Ground, the 21-year-old has made 20 appearances in all competitions, one of them coming in the FA Cup tie with Arsenal earlier this month.
Having made a positive impression during that fixture, The Mirror suggests that the Gunners are interested in signing the right-sided player.
The report claims that Arsenal would have to shell out in the region of £10m for Spence, who has 18 months remaining on his contract.
However, having also represented his parent club in August, the Englishman is ineligible to play for another team this campaign, ensuring that he will remain at Forest until May.