A poor showing in the Six Nations and criticism around his coaching methods has made Jones' future uncertain.
UK media has touted Robertson as the perfect replacement.
Woodward - who led England to their 2003 World Cup victory - told Martin Devlin what makes the current Crusaders coach special.
"Clearly, he's a winner, he's successful, he's very good with people."
He says that Robertson would "love it" if he got the job.
"I just get a really good feeling about him. Even though I'm kind of old now, would I like to play for him? Yes, without even knowing him, just from seeing the way his team plays."
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