The Warriors will be Scotland's sole representatives in the inaugural Magners League Play-Offs and will travel to the Liberty Stadium in Swansea to play the champions of 2005 and 2007 on Friday 14 May (kick-off 7.05pm - live on BBC Wales & BBC Radio Scotland) - the biggest game in the history of the Warriors to date.
At present, Glasgow supply the majority of the Scotland team and the Ospreys' 38-man registered squad contains 26 internationalists from around the globe.
With such quality on show, Lineen is preparing his charges for a match of Test-level intensity.
"This is an international for us," he said, "but as it stands, they are the favourites with home advantage.
"These are exciting times for the club but we are under no illusions how challenging this task is.
"The Ospreys squad is chalked full of quality players with eight British Lions and three All Blacks."
From the match-day squad that featured in last Friday's 37-32 bonus point win over the Scarlets, the Warriors welcome back centre Max Evans and flanker John Barclay.
The only absentee is hooker Dougie Hall who sustained a dislocated thumb. As a result, Pat MacArthur is included in today's 25-man draft.
Glasgow Warriors squad to play the Ospreys in the Magners League semi-final Play-Off at the Liberty Stadium on Friday 14 May (kick-off 7.05pm - live on BBC Wales & BBC Radio Scotland):
Backs: Chris Cusiter, Rob Dewey, Max Evans, Peter Horne, Mark McMillan, Graeme Morrison, Hefin O'Hare, Dan Parks, Colin Shaw, Bernardo Stortoni, DTH van der Merwe, Duncan Weir
Forwards: John Barclay, Tim Barker, Johnnie Beattie, Ed Kalman, Kelly Brown, James Eddie, Calum Forrester, Alastair Kellock, Moray Low, Pat MacArthur, Fergus Thomson, Kevin Tkachuk, Dan Turner
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