United have been heavily linked with a move for Alderweireld during the current transfer window due to the Belgian's uncertain future in North London beyond next season.
Alderweireld's current contract includes a £25m release clause which will be triggered next summer, and talks over a new deal have so far proved fruitless.
Spurs are therefore considering cashing in on the 29-year-old with United favourites for his signature, but the Manchester Evening News reports that club scouts have developed concerns about the player.
United are thought to value Alderweireld at around £50m - some £20m below Tottenham's asking price - but could now prioritise other targets in their bid to bolster their defensive options.
United are not planning to sell any of their current centre-backs this summer either, meaning that six players could be battling it out for two places next season.