The Kop boss has refused to deny that he might look to bring the free-agent former Real Madrid and Newcastle striker back to the club he left in 2004.
The former England striker is a free-agent after being released by Manchester United after three-years with the Old Trafford club but is yet to sign up with another club.
He has been heavily linked with Stoke City throughout the summer, and in more recent times with Martin O’Neill’s Sunderland however he is yet to announce where his future lies.
And following Andy Carroll’s loan move to West Ham United, there has been speculation that Liverpool could make a move for Owen to help boost their attacking options.
And when quizzed by reporters following his side’s 2-0 home loss to Arsenal on Sunday, Rodgers refused to deny he is interested in the 32-year-old.
He also admitted that if he realized the club would not be adding to its attacking options, he would not have allowed former Newcastle front man Carroll to leave the club.
Rodgers said: "Any player that I believe can improve the squad I will look at. We have got a very, very small squad with some very young players in it. So I can't say no."
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