Van Nistelrooy is available after being pushed out of United by new manager Ruben Amorim this week.
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Talksport says the former striker has applied for the job at Coventry City .
The Championship club are in the hunt for a replacement for Mark Robins, who was sacked as manager earlier in November.
Former Chelsea midfielder Frank Lampard is also set to hold talks about the Coventry job.
The club is currently in seventeenth place in the Championship table.