United are understood to be very keen on the 28-year-old defender, who has one year left on his contract at the Emirates Stadium.
Vermaelen is Arsenal captain, but was limited to just seven league starts last season with Arsene Wenger preferring a centre-back pairing of Laurent Koscielny and Per Mertesacker.
Arsenal are keen to offer Vermaelen fresh terms, but the player is now set for talks and seems likely to seek a move away from the club he joined from Ajax in 2009.
Now following Belgium's departure from the World Cup finals, Vermaelen is turning his attention to his future.
"I really do not know where I will play, Arsenal or elsewhere next season," he is quoted by the Evening Standard.
"All my attention went to the World Cup. I will see when I talk with Arsenal."