Reports in Sweden claim United are keen on signing Grankvist on loan deal in January - similar to the one they sanctioned for his compatriot Henrik Larsson in 2007 - as Jose Mourinho looks to bolster his defensive options.
Grankvist currently plays for Swedish second tier outfit Helsingborgs IF.
Mourinho has publicly voiced his frustration over the lack of investment given to him, in particularly the ability to strengthen his defence.
The Portuguese demonstrated this by naming youngster Scott McTominay in the starting lineup against West Ham, despite having Eric Bailly available for selection.
Asked about interest from Old Trafford, Granqvist told 'FotbollDireckt': "I know that there is a lot of interest for me. United is incredibly flattering but I have not heard anything concrete yet."
Granqvist has experience playing in England - he spent two seasons playing for Wigan before moving to Dutch side Groningen.