The Real Madrid star is on the verge of signing for the Red Devils for a reported British-record fee of around £65 million.
It is unclear where the Argentina international will fit into Louis van Gaal's 3-5-2, although despite being primarily a wide-man, Di Maria played in the centre of midfield at times for Los Blancos last term.
Robson, who played in midfield for the Gunners back in the 1980s, has admitted that he is unsure where Di Maria will play should he complete a switch to Old Trafford, but he thinks that Mata will have cause for concern.
The Spaniard arrived for a club-record fee of £37.1m from Chelsea back in January, but he could make way for Di Maria's inclusion in the starting line-up, according to Robson.
He told talkSPORT: "I’m not sure where Di Maria is going to fit in. The only thing I can think of is he would take the place of Juan Mata, playing as a player in between the midfield and front players, or he could play out wide if they played with a 4-3-3.
“I can’t see him fitting into the side at the moment without taking Juan Mata’s place. It isn’t working for [Mata]. I can understand the problems Jose Mourinho had with him. Juan Mata can only play in a side that is completely dominating the play.
"He is very creative in the top third of the field but he doesn’t like it when there are big, open spaces because he is not a particularly good athlete, whether he is counter-attacking, having to run with the ball or he is having to defend in big, wide open spaces.
“He is a much better player when he is playing in a team like the Spanish Under-21s. When he was playing for them they were dominating play and he could pick out his passes in the top third and be clever with his movement and his one-twos."
The move for Di Maria has caught many people off guard. Their need for defensive reinforcements has been paramount for most of the summer following the departures of Rio Ferdinand, Nemanja Vidic and Patrice Evra.
And with Van Gaal set to continue with a three-man backline, the move for a £65m-rated attacking player has raised eyebrows, despite the undoubted quality that Di Maria possesses.
Marcos Rojo was brought in last week for around £16m, but the Red Devils have been forced to use academy graduate Tyler Blackett in both their Premier League games so far.
The 20-year-old is certainly one for the future, but being asked to play in defence at a time when United are trying to get to grips with a new regime following last season's harrowing campaign is a difficult task for the young defender.
United followed up last week's opening day defeat to Swansea City with a 1-1 draw away to Sunderland, and Van Gaal is expected to continue his spending before the September 1 transfer deadline.
Ajax's Daley Blind has been linked with a move, while Nigel de Jong is also a reported target.