The ex-Ajax, AC Milan and Barcelona forward - currently at PSV Eindhoven - has already had a spell in England when he spent the 2004/05 season with Newcastle.
Owls manager Brian Laws confirmed the Championship club have invited the 31-year-old for a trial but played down its significance.
Laws told BBC Radio Sheffield: "I have a strong contact in Holland who is Kluivert's agent.
"We've invited the boy down, and I want to run the rule over him. It is just a possibility and is nothing concrete at the moment - but we've made an inquiry."