They travel to Swansea tasked with trimming what is currently a five-point gap between them and the Welshmen, with reigning champions Munster sitting in third.
Glasgow's best result at the Liberty Stadium to date is a 9-9 draw in 2009, but they won the first meeting between the teams this season 28-17 at Firhill last October.
Lineen told www.glasgowwarriors.org: "Every game between now and the end of the season is one where the stakes are well and truly raised, and the players are excited by the challenge of doing something we've never managed before: winning away to Ospreys.
"It's a place where you have to be really strong both physically and mentally, because you can be absolutely sure the Ospreys will.
"The last couple of games show that the team have come a long way this season in terms of our ability to stick in and put ourselves in a positive position. What they've also told us is that we need to make good decisions more consistently to convert those opportunities into wins.
"It's about thinking on our feet, not letting the pressure of the situation get to us, and realising that one bad call can be the difference between a win and a draw, or a draw and a defeat, in the sort of tight match we've been experiencing.
"If we get that part of our game right, we're more than a match for any team in this competition."
There are four changes to the Warriors starting line-up, three in the pack and one behind the scrum. Lineen has continued to rotate his hookers, Dougie Hall selected to start the game.
In the second row, Al Kellock has been made available by Scotland and will captain the side. Calum Forrester will start at blindside flanker.
In the centres, meanwhile, Federico Aramburu will partner Alex Dunbar, with Troy Nathan forced to sit the game out with a back injury.
Lineen explained: "It's another strong side we're sending out. It's a marker of the strength in depth we're developing that even with ten backs unavailable for one reason or another, there's still plenty of quality and tenacity behind the scrum.
"We're obviously really pleased to have Al available - he's chomping at the bit to get stuck into what he and the rest of the guys know is a truly massive game for us all.
"As ever, we need everyone to perform and everyone to make good decisions."
After Friday's trip to Swansea, Glasgow Warriors put their RaboDirect PRO12 play-off credentials on the line in a Firhill clash with Italian side Aironi on Friday 23 March (kick-off 7.35pm).
Tickets for this potentially season-defining game are available NOW via www.glasgowwarriors.org, by calling 0844 800 3490 or in person at the Gordon Street and Sauchiehall Street branches of Greaves Sports, our official retail partner.
Book in advance online or over the phone to get an adult ticket for just £15, a £5 saving on the match-night price.
Students/senior citizens £10, under-18s £5.
GLASGOW WARRIORS TEAM TO PLAY OSPREYS IN THE RABODIRECT PRO12 AT THE LIBERTY STADIUM ON FRIDAY 2 MARCH (KICK-OFF 7.05PM, LIVE ON BBC ALBA)
15 Peter Murchie
14 David Lemi
13 Alex Dunbar
12 Federico Aramburu
11 Colin Shaw
10 Ruaridh Jackson
9 Henry Pyrgos
1 Ryan Grant
2 Dougie Hall
3 Jon Welsh
4 Tom Ryder
5 Al Kellock (CAPTAIN)
6 Calum Forrester
7 Chris Fusaro
8 Ryan Wilson
SUBSTITUTES
16 Pat MacArthur
17 Gordon Reid
18 Ed Kalman
19 Rob Verbakel
20 Scott Wight
21 Murray McConnell
22 Johnnie Beattie
23 Tommy Seymour
Not considered for selection due to injury: Mike Cusack (sickness), Rob Dewey (shoulder), Moray Low (knee), Troy Nathan (back), Fergus Thomson (shoulder), DTH van der Merwe (shoulder).
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