The 63-year-old man thought to be Neville Neville was bailed until May pending further police enquiries.
Mr Neville's two sons Gary and Phil both played football for Manchester United and England while daughter Tracey played netball for England.
He is a former director of Bury Football Club, where wife Jill is still club secretary.
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The police officer was shot in the arm at a petrol station on the Crumlin Road, but is in a stable condition.
Temperatures tumbling again tonight with a widespread sharp frost and lows of -5C or -6C and icy spots in places
The victim was shot in the arm in a 'drive-by' shooting.