"The Connacht game isn't a 'must win', it's a 'can win'," he said ahead of their departure for Galway.
"They beat us last year over there in stormy conditions and they'll be hurting after a heavy defeat to the Scarlets last week. Connacht will be targeting this as a win but so will we."
Lineen has made four changes to the team that lost to the Ospreys last Friday with Opeta Palepoi replacing the injured Tim Barker (back) in the second row and Stevie Swindall comes in for Kelly Brown at blindside flanker. As a result, Brown moves to No. 8 and Johnnie Beattie drops to the bench.
In the backs, Max Evans has recovered from a dead leg to replace Andrew Henderson whilst Hefin O'Hare takes his place on the right wing ahead of Lome Fa'atau.
Glasgow Warriors team to play Connacht in the Magners League at the Galway Sportsground on Friday 19 September (kick-off 6:30pm)
15 Bernardo Stortoni
14 Hefin O'Hare
13 Max Evans
12 Graeme Morrison
11 Thom Evans
10 Dan Parks
9 Mark McMillan
1 Justin Va'a
2 Dougie Hall
3 Moray Low
4 Opeta Palepoi
5 Alastair Kellock CAPTAIN
6 Stevie Swindall
7 John Barclay
8 Kelly Brown
Substitutes
16 Eric Milligan
17 Kevin Tkachuk
18 Dan Turner
19 Johnnie Beattie
20 Andrew Henderson
21 Colin Gregor
22 Ruaridh Jackson
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