Ramsey has impressed for the Gunners this season, scoring 11 goals in just 16 appearances.
“I was very close to signing Aaron at Everton. He was in my house but Arsenal beat me too it,” he said.
“He’s played really well, he’s improved. He maybe now sees himself as one of the really important players and that can help players.
“He’s certainly not letting them down with the goals he’s scoring.”
Manchester United face Arsenal at Old Trafford on Sunday.