According to Adrian Kajumba of the Daily Mirror, 14 teams are taking a look at the England youth international, whose contract is set to expire at the end of the 2017-18 Premier League season.
As well as Arsenal and Chelsea, Tottenham Hotspur, Watford, Stoke City, West Bromwich Albion and Southampton are reportedly keeping an eye on the situation, as well as a number of outfits from the Championship.
The 20-year-old is on loan at Shrewsbury Town and has enjoyed a strong start to the season. As Ladbrokes noted, the goalkeeper's loan team have proved difficult to beat:
While it's still early in the stopper's career, Henderson is approaching a point when he will want to play games every week at a high standard.
He's unlikely to get that at United, with the world-class David De Gea, the dependable Sergio Romero and promising Joel Pereira ahead of him in the pecking order.
He was recalled from a loan spell at Grimsby Town last term because of injury issues with the first-team options, per Simon Peach of the Press Association:
For the time being, it's understandable the youngster is keeping his options open, as he's evidently enjoying getting regular football at Shrewsbury.
Having emerged through the United youth setup, leaving the club would be a big decision. However, some of the aforementioned sides would not only be able to offer Henderson a new challenge but also a clearer path into the first team and the chance to show his talents on a big stage regularly.
At United, regular football feels a long way off for Henderson regardless of how well he does at New Meadow. Given his clear potential, the Red Devils would ideally like to keep him around, but with so much interest in the goalkeeper, there will surely be an offer that tempts the England youth international away from Old Trafford.