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The former United defender has urged the Portuguese to persuade Ozil to move to Old Trafford.
The Red Devils have been linked with the Arsenal star with his contract running down.
While they face competition from Barcelona, Ozil could well reunite with Mourinho at United.
And after his latest contribution for the Gunners, Neville feels it is time to act.
Ozil struck home a superb volley for Arsenal in their game with Newcastle today.
The German opened the scoring, continuing his strong run of form in an Arsenal shirt.
Mesut Ozil's club at the end of the January transfer window: Latest odds
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“What a goal from @MesutOzil1088 sign him Jose”
Phil Neville
And Neville subsequently tweeted his message to Mourinho: “What a goal from @MesutOzil1088 sign him Jose”.
The tongue-in-cheek comment will only add fuel to the fire surrounding a potential controversial switch.
Arsenal will be powerless to stop Ozil heading to Manchester at the end of the season.
And they may even opt to sell in January if they fail to persuade him to sign a new deal.
Mourinho refused to rule out an approach for Ozil this week, with the boss seeking new additions to his United squad.
With Henrikh Mkhitaryan’s future in doubt, a playmaker is likely to be on his agenda too.