The Dragons are in the final eight of the European Challenge Cup where victory would mean an automatic entry into the Heineken Cup competition. They are also battling their regional rivals for a berth via the Magners League. The Dragons are already a point ahead of the Scarlets in the Magners League table. Victory over Glasgow would guarantee them sixth place and see them breathing down the necks of the Ospreys and Blues.
"We were very disappointed not to qualify for this year's Heineken Cup but the Challenge Cup has been very good for us and we've got a big quarter-final to look forward to. However, the Heineken Cup is where we want to be competing," said Owen.
"People wrote us off at the start of the season but things are rarely as bad as people make out and we are playing some good rugby. You look at the table and there is so little to choose between top and bottom so we'll just keep fighting to the end."
In such a competitive league, home advantage has proved crucial to the Dragons' improved form this season, having gone five months unbeaten at Rodney Parade.
In other Dragons news, staying at the Parade for another two years is Wales lock Luke Charteris, 23, who has signed a two-year extension to his contract with the Dragons just days after second-row partner Ian Gough confirmed he will be joining the Ospreys.