The Glasgow coach has named an unchanged side for the clash against Wasps - who have not lost at home in the Heineken Cup in 12 games.
Glasgow haven't won on the road in three games but Lineen has called on his side to grab the opportunity to record back-to-back wins with both hands.
"We need to look at this game and go 'what an opportunity'. This is the first time for so long that Glasgow have won their first-up Heineken Cup game," said Lineen.
"So for us this represents something special - maybe we can make a bit of history. We know going down there it is going to be incredibly difficult.
"Wasps are a quality team with a lot of pedigree behind them in the Heineken Cup. They have quality individuals with a lot of belief and are a physical team."