The Red Devils are thought to be closing in on Real Madrid's Alvaro Morata in a deal worth over £60m.
Defoe moved to Bournemouth on a free transfer earlier this week after leaving Sunderland.
And with United set to spend big, Saunders thinks they've missed a trick.
Saunders told talkSPORT: "I would have taken Defoe.
"He's 34, scored 15 goals last season, [has a] couple of years in him. His instinct of getting to the ball first in the box is brilliant.
"You're gambling, every time you sign a striker from abroad it's a gamble.
"I don't think it's a gamble with Defoe.
"Jermain Defoe is my favourite player. I love watching him.
"I like how his brain works and how he can finish, he finishes all types of chances.
"He doesn't drink, he's fit as a fiddle. He will (start) if he scores every week."