The 22-year-old has struggled to shake off persistent muscle problems since joining the Catalonia giants in 2017, and Barcelona are said to be willing to allow him to fashion an exit this summer.
But the Premier League clubs will also examine the reasons behind Dembele's injury-plagued spell in LaLiga before making their interest official.
Diario Sport claim that United and Arsenal will undertake an evaluation of the reasons behind Dembele's time off the field, to avoid the star being hampered with similar injuries should he secure a move to England.
Barcelona may even allow Dembele to leave for a rumoured £43million, with the club hopeful of garnering money to pursue their targets when the transfer window eventually re-opens.
Any potential deal would represent a sizeable loss for the LaLiga champions, who originally splashed out an initial £96.8m fee to secure him from Borussia Dortmund.
However, the interested parties are also thought to view Dembele as a talent too good to pass up if he were to become available - and both United and Arsenal are hoping to bolster their attacking options at the end of the season.
The same report hints that a loan switch may be an option, with Barcelona open to exploring several avenues in order to cut their losses.
Dembele has reportedly even contacted France team-mate Anthony Martial in order to gain inside knowledge into life at Old Trafford.
But the winger is also believed to be willing to remain at Barcelona and battle to secure a first-team spot once again.
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