The Gunners were hunting a new boss after sacking Bruce Rioch.
But legend Robson U-turned on his decision at the 11th hour and decided to stay at Porto instead, according to The Times.
Former England manager Robson was 63 when the Gunners made their approach.
He did leave Porto that year but instead agreed a move to Spanish giants Barcelona.
After being snubbed by Robson, Arsenal chiefs then set about drawing up a list of alternatives, identifying Wenger as their possible man.
Gunners vice-chairman David Dein had met the Frenchman in 1989 and had been impressed with his work as Monaco boss.
His appointment, which came 20 years ago last week, was met with a degree of scepticism by Gunners fans.
Wenger had been managing Nagoya Grampus Eight in Japan before moving to London and was seen as a low-profile appointment.
He has gone on to become the most successful manager in the club’s history – despite having failed to win a Premier League title for 12 years.
The 66-year-old is out of contract at the end of