Former United boss Sir Alex Ferguson wanted to bring Adams to Old Trafford before Arsene Wenger took over as manager for the Gunners.
Adams rejected both attempts by United to sign him.
“Alex Ferguson wanted to sign me twice, just before Arsene Wenger came to the club,” said Adams.
“I was ready for a change and he was onto me every day.
“The chairman at the time, Peter Hill-Wood, convinced me that there was a good man on the way and that we were going to be ambitious financially.
“I found my salary tripled, which was amazing. Arsene came and the rest is history.”