The English centre-back was deemed surplus to requirements at United, but Nicholas thinks he could have done a job for Arsenal.
"Arsenal don't sign personalities," Nicholas told Sky Sports.
"Sadly I have to go way back to David Dein and he would sit down with Arsene Wenger and ask what kind of character he was signing. That's gone now. It's as if Arsenal sign players because they are desperate.
"They could've had Cahill from Chelsea and sat him in the defence. He is better than what they have and is also a leader, but they missed out."