British newspapers had reported that Real Madrid were willing to pay 10 million pounds ($18.41 million) for Owen as well as sending Fernando Morientes or Samuel Eto'o to Anfield as part of the deal.
Had he played in Graz, Owen would not have been able to play in Europe for any other club this season, slashing his transfer value. Owen's Anfield contract expires at the end of the season.
Owen stayed on the substitutes' bench for new coach Rafael Benitez's first competitive match in charge as Liverpool dominated the third qualifying round, first leg match.
Asked about his line-up, an evasive Benitez told Britain's Channel Five television: "When I decide the starting XI, it's because I have confidence in the players.
"We have four good forwards and today I played two of them (Djibril Cisse and Milan Baros)."
Pressed about whether Owen would remain a Liverpool player, he told reporters: "I can't predict the future. I'm only concentrating on the present and our performance tonight, which was good.
"At the moment Michael is one of our four forwards... I don't want to say anything else."
A Real spokeswoman said on Tuesday the club had nothing to say about the reports, and Spanish media were uncharacteristically reluctant to take up the tale.
Marca, one of two Spanish sports dailies with close links to Real, noted the rumours but said Real directors had flatly denied any interest in signing Owen, a former European Player of the Year.
It would be unwise to take any Real denial at face value, however, given the track record of president Florentino Perez over recent seasons.
Perez strongly denied any interest in signing David Beckham -- "Never, never, never," was his famous refrain -- a few months before agreeing to pay Manchester United 35 million euros ($42.97 million) for the England captain.
Perez was similarly coy about confirming the club's previous big-name signings, Luis Figo, Ronaldo and Zinedine Zidane, before they were poached from their clubs.
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