Rodgers is lacking attacking options and Owen is currently available as a free agent.
"Any player that I believe can improve the squad I will look at," Rodgers said. "We have got a very, very small squad with some very young players in it. So I can't say no."
Rodgers added: "We all know we needed reinforcements and the players needed help but it's gone now and I can't do anything about it.
"There is no point in me sitting here crying about it wishing we had or we hadn't. There is no doubt the finances here had to be changed. That is the reality. We have lost nine players and brought in three so from a business side the club has done well. What we need to do well for the future now is look after the football business and help the players here."