Ferguson turned down the opportunity just months before taking charge at Old Trafford.
Ferguson wanted to take compatriot Walter Smith with him to London.
He said: “I was offered the Arsenal job and I wanted to take Walter with me.
“I thought I would sound him out when we were on Scotland duty together. We were going to play in Israel and I didn’t know that Walter was going to Rangers at that time.
“I told him that I had been offered the chance to go to Arsenal and I asked him what he thought. He was positive about it, saying they were a big club and that kind of thing.
“So I said to him ‘Do you fancy coming with me?’ Then he dropped the bombshell that he was going to Rangers.
“The thing about the Arsenal offer was that they wanted an answer right away but I couldn’t give them one because I was going to the World Cup in Mexico with Scotland.
“So the Arsenal thing fell by the wayside. Walter went to Rangers and then later that year I went to Manchester United.”
