Reds boss Jose Mourinho has been heavily linked with a move for the Gunners star, who will be available on a free transfer at the end of the season unless he pens a new deal.
There had been suggestions that Mourinho's interest had gone cold following the German's poor form for the Gunners this season.
However Ozil showed what he is still capable of with a stunning display in Arsenal's 2-0 win over Tottenham on Saturday, which is sure to have caught the eye of the United boss.
There will be strong competition though as his former club Schalke could offer him the chance to return to the Bundesliga.
The 29-year-old began his professional career at the Veltins-Arena and turned out for Die Konigsblauen 39 times in all competitions before making the switch to Werder Bremen in 2007.
Schalke's supervisory board head Clemens Tonnies says they are interested but does not feel he will re-join Die Knappen just yet, which puts United in the box seat, although there is talk that Barcelona are also keen.
"I still have a great relationship with Mesut," he told kicker. "We would definitely consider it. If it fits for both sides, it would be nice.
"The player could say that he returns to his roots, and that he plays football in this stadium and for those fans and the region once again. But it will certainly not happen next season."