Kinnear admitted: "I don't want to lose any of our best players. The clock is ticking to January but the clock is ticking for me too.
"Will I have any influence over him? If I am still here, yes. I hope that I could keep him.
"I have a perfect relationship with him. It is understandable that other clubs are interested. He is 28, has bags of ability and can score goals. There must be dozens who want him - dozens.
Owen's current deal runs out this summer and the England striker is yet to sign an extension.
Kinnear, who takes his men to Fulham tomorrow, added: "At the moment, the club is trying to be sold so I don't know if anyone is going to sit down with Michael.
"It might be a case of 'We don't know where we are going. Whoever comes in, it's their problem'."