The Algeria international has been a star performer in Serie A in recent years, but his capture would put incumbent Red Devils left-back Luke Shaw's long-term prospects at Old Trafford in doubt.
Italian outlet Radio Kiss Kiss Naples (via CalcioMercato.com) reported the Red Devils could make a huge offer for the left-back in an attempt to strengthen their options in the winter (h/t Rebecca Coles of The Sun).
An effort to sign Ghoulam would not have been a surprise in the summer with Shaw on the fringes of the first team, but the England international has been one of United's few success stories of the campaign.
United manager Jose Mourinho has brought Shaw out of the cold this term and he has performed well, but his contract expires next summer.
The Algerian has yet to make an appearance this season after struggling with a knee injury suffered in the 2017/18 season, but he was a regular starter with the Partenopei before the issue. He made 26 league starts in the 2016/17 season, and at 27 he is the type of experienced player the Special One craves.
Ghoulam's potential arrival could damage Shaw's hopes at United while Mourinho remains at the helm.
The 23-year-old was one of the best prospects in Europe as a teenager at Southampton, but injury and poor form have cost him vital minutes in the starting XI.
Shaw recently thanked supporters for sticking with United after the team fought back from 2-0 down to beat Newcastle United 3-2 at home in the Premier League:
However, there is the chance Mourinho could team up Shaw and Ghoulam, with the Napoli star playing ahead of the defence.
The player was directly involved in five goals in Serie A and Europe for Napoli last term in just 17 appearances, underlining his attacking nature on the wing.
Marcus Rashford and Anthony Martial typically opt to cut inside from the left wing, rarely crossing the ball for others in the middle.
Ghoulam and Shaw could be an intriguing combination, but with Shaw's contract close to expiring, United could be looking to secure the Englishman's replacement.