Both players are thought to be on United's radar as Louis van Gaal looks to strengthen his squad ahead of next season.
And the Sunday World now claims that both players have 'tentatively agreed' to make the move to Old Trafford.
Manchester United have reached tentative agreements with Mats Hummels and Memphis Depay
It is suggested that executive vice-chairman Ed Woodward has gained assurances from both players that they will join the Red Devils at the end of the season.
Woodward has been criticised for leaving his transfer dealings to the last minute in the past - particularly during David Moyes' time in charge - but he has reportedly moved quickly to tie up deals ahead of the summer transfer window this time around.
Hummels said yesterday that he was looking to keep his options open with Dortmund keen to tie him to a new contract.
GETTY
Memphis Depay is wanted by Manchester United
And there seems to be a growing acceptance from PSV that they will lose Depay to a big club in the summer after his impressive season in the Eredivisie.
The reports claim that United are also hopeful of tying up a move for Southampton's Nathaniel Clyne in the near future, while they will step up their efforts to secure a replacement for Radamel Falcao who won't be retained when his loan deal comes to an end.
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