The former England striker is available on a free transfer after being released by Manchester United this summer.
The 32-year-old has been linked with a number of clubs, including Stoke City, Sunderland and Celtic, though he is yet to make a decision on his future. Following Andy Carroll's season-long loan to West Ham United, there have been rumours that Owen is an option for Rodgers to boost attacking options at Anfield.
When quizzed by reporters, Rodgers refused to deny interest in Owen: "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."
Owen left Liverpool in 2004 to join Real Madrid.