And nor should fans of the north London side be - as far as he is concerned.
Indeed, Barton thinks the Gunners should be wary of buying anyone from a 'Manchester United fire sale.'
According to the 31-year-old, no player ever improves after being purposely sold by Man United, tending to instead depreciate in value or ability.
@themichaelowen I'd be wary of buying anyone from a Man Utd fire sale. They tend to never produce anywhere near the levels they do at OT!— Joseph Barton (@Joey7Barton) September 1, 2014
Barton later added that Paul Pogba, who is now flourishing at Juventus, was not sold out of choice by Manchester United but, rather, opted to leave the Red Devils himself.
I am not saying they all don't do well. I'm saying I would be wary they TEND not to sell players who get better!— Joseph Barton (@Joey7Barton) September 1, 2014
Welbeck moved to the Emirates Stadium on Deadline Day, with a £16 million fee quoted.
Manchester United have also loaned Javier Hernandez to Real Madrid and brought Monaco striker Radamel Falcao to Old Trafford on loan.
It should be interesting to see how Welbeck fares at Arsenal, with Arsene Wenger desperately needing a solution to his striker struggles.
Wenger brought Alexis Sanchez to north London for £35m this summer, though the Chilean is not a natural centre-forward. Yaya Sanogo, meanwhile, has performed poorly for the Gunners while deputising for Olivier Giroud, who is out until the new year with a broken foot.
Barton's comments, of course, will likely be put to the test as England striker Welbeck is only 23. His form may just determine how far Arsenal are capable of going this season.
Should Arsenal be wary of buying a player not wanted by Manchester Untied?