The former Denmark international took over at the Liberty Stadium following the departure of Brendan Rodgers to Liverpool in the summer.
"He'll keep them up without doubt," BBC Sport quotes Rush as saying. "Swansea did really well last season and they'll stay up because of the football they play. I'm looking forward to seeing him. He's a lovely man and a great manager."
Rush played alongside Laudrup during the Welshman's season at Juventus in 1987.