Owen is available from Manchester United.
Wright wrote in The Sun: "I still feel he has something to offer at Premier League level but he needs to be less concerned about wages and focus on getting game time.
"In a few years, I wonder what people will remember of Owen. He is a player I really admire and it would be great if they recall he recorded 40 goals in 89 games for England.
"At the moment, Owen will be seen as enjoying a fantastic early career but it ending as a damp squib and I really hope he addresses this issue.
"He still has the time and ability to do it. But he needs to play regularly and I think Rodgers would be put off by some of the baggage Owen may be carrying."