Should they avoid defeat once more they would set a new club record in the RaboDirect PRO12 of seven matches unbeaten, but Lineen is wary of the threat posed by the free-scoring Gunners.
And as he prepares his side for a 1872 Cup double-header, Lineen is refusing to live on past glories.
"It's pleasing to know we've found a measure of consistency, but stats go out the window the minute the next game kicks off, particularly when it's a derby," he said.
"It's a measure of the competition we've got at the moment that each week a number of guys can feel justifiably aggrieved at being left out, but as a coaching team we've shown that players will get their opportunity if they keep working hard, and that's very much the case here again.
"As ever, the derbies are two huge matches in our season. We all take great pride in representing Glasgow and the west of Scotland against our local rivals, but the overriding priority is claiming more RaboDirect PRO12 points to further our aspirations in the tournament."
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