Their preparations for this round 3 fixture have not been ideal, with a lengthy injury list forcing Monday's on-field training session to be cancelled.
In terms of the extended squad, the likes of new signing Darragh Fanning, Aidan Wynne and Academy player Shane Conneely are again pushing for selection.
Injuries permitting, Elwood may opt not to tinker with the 23-man panel that was on duty for last weekend's agonising 35-33 loss to the Scarlets.
That depends on whether Ray Ofisa (neck), Troy Nathan (shoulder), Jamie Hagan (hamstring), Miah Nikora (dead leg), Bernie Upton (head) and Niva Ta'auso (hand) can recover in time from their respective knocks.
Both Connacht and Glasgow have been troubled by injuries in the opening weeks of the new season.
Team captain John Muldoon (broken arm), Johnny O'Connor (back), Robbie Morris (back) and Ezra Taylor, a recent debutant against the Newport Gwent Dragons, head the province's longer term injury list.
Taylor sustained medial ligament damage in his knee during the bonus point win over the Dragons, and is expected to be sidelined for six weeks.
Eoin Griffin (broken metatarsal) and Conor O'Loughlin (shoulder) are also currently receiving treatment.
Elwood said: "We are aiming to pick our strongest team. We feel there are points to be got from the Glasgow game, and if we have to taper our sessions to field the best team, we will.
"It's important for us. In certain positions we don't have options, so it is important to give the guys a rest to enable them to play.
"Glasgow is always a tough place historically. They are battlers, a very physical team with a good set of forwards that compete at the breakdown.
"They work hard in defence and are very committed, so we will not get anything easy," he added.
CONNACHT Squad (v Glasgow Warriors) - Backs (12): Cillian Willis, Frank Murphy, Miah Nikora, Ian Keatley, Fionn Carr, Keith Matthews, Niva Ta'auso, Tiernan O'Halloran, Aidan Wynne, Troy Nathan, Gavin Duffy, Darragh Fanning.
Forwards (14): Ronan Loughney, Brett Wilkinson, Sean Cronin, Adrian Flavin, Rob Sweeney, Jamie Hagan, Andrew Browne, Dave Nolan, Michael Swift, Bernie Upton, Michael McCarthy, Ray Ofisa, Mike McComish, Shane Conneely.