The 21-year-old showed signs of real promise during his short-term spell at Bramall Lane last season, and bagged two Championship goals in the Blades' stellar 2018/9 campaign - including the winning goal in a Man of the Match performance against West Bromwich Albion.
The Sun have claimed that the Toffees are eager for Dowell to continue his development away from the club next season, as the glut experienced midfield options at the club would make it tricky for the youngster to earn a regular starting spot.
It is unclear whether the Blades are looking to bring to the club for the upcoming season, but their limited number of midfielders could see United boss Chris Wilder make a fresh move for the England U21 international.
However, the report suggests that Wigan Athletic and Huddersfield Town are the front-runners to bring in the dynamic midfielder, as they are more likely to afford the player a starring role in the second tier than the Blades are in the Premier League.
Last season, Dowell played both in the central midfield and attacking midfield role for the Blades, and proved a useful and versatile option throughout the campaign. With Luke Freeman arriving on a club record deal last week, United should have the latter position covered between the former Arsenal starlet and Mark Duffy. Argubaly, Dowell lacks the strength to operate in a deeper position, which suggests that another spell at Bramall Lane could be unlikely.