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 team.
He has been heavily linked with Stoke City throughout the summer, and in more recent times with Martin O'Neill's Sunderland and Scottish Champions Celtic, but 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.
When quizzed by reporters following his side's 2-0 home loss to Arsenal on Sunday, Rodgers refused to deny he is interested signing the 32-year-old.
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Rodgers said: "Any player I believe can improve the squad I will look at. We've got a very small group, 19 players training yesterday morning, and some very young players in and amongst that.
"I can't say no [about Owen], I always have to look and see where we can improve the group."
Former Liverpool midfielder Jamie Redknapp is backing the move after what he said was a "disastrous week" for Liverpool in the build up to transfer deadline day, and says the club have put themselves in a difficult position by not replacing Carroll.
"If I was them the first thing I would do is go and get Michael Owen now," he told Sky Sports. "He is free agent. They need to do something because at the moment there are real problems for Brendan."
"It has been a disastrous week. People talk about the plan B; the plan B is now at West Ham. What they have done this week and the pressure Brendan Rodgers has put himself under, by letting Andy Carroll go, is beyond me.
"It is almost like you are playing roulette. If you are not going to a replacement you have to get Clint Dempsey but they have not got him so you keep Andy Carroll.
"Anybody who was watching West Ham yesterday, and particularly Liverpool fans, will be thinking, 'what are you doing?' Borini and Suarez are Liverpool's only recognised forwards. They have put themselves in a really difficult position now."