The Italian capital club will be on the lookout for a new defender in the summer.
The 20-year-old has impressed at PSV Eindhoven on loan this season.
The Dutch club are also eager to secure Branthwaite permanently at the end of the term.
Per Giallorossi.net, Branthwaite stands out among the targets for Roma for their defense.
Manager Jose Mourinho is a huge admirer of the left-sided defender.