Interim boss Cullie Tucker knows Connacht's play-off fate is out of their hands but wants his side to go down fighting.
The Westerners, who parted ways with head coach Pete Wilkins in April, sit 14th in the table with two rounds remaining.
They can mathematically sneak into the top eight but need to win both remaining games, starting with the visit of Edinburgh this evening and a trip to Zebre, and then hope other results go their way.
They boast a mixed record at the Dexcom Stadium this season, winning four and losing three games, and are without Lion Mack Hansen and out-half Jack Carty, who both have ankle injuries.
The 2016 Pro12 winners are also on a losing run of four games in the tournament, the last two of which came in South Africa, against the Lions and Stormers.
"We know our play-off hopes are out of our own hands, but that's not stopping us doing everything we can to finish this season strongly," said Tucker, who has named Bundee Aki in the centre this evening for his 150th Connacht cap.
"We're aiming for 10 points across these final two games, starting against a tough Edinburgh side, and then whatever happens happens after that.
"Our supporters have been brilliant to us, especially during the more difficult times, so for this final home game we want to give them something to cheer for.
"It's also the final Dexcom game for a number of our departing players, so we want to pay tribute to them in the right way, both on and off the field. So it should be a great occasion and we're looking forward to the challenge"
Edinburgh, meanwhile, have won their last two matches in Ireland and are bidding for a first three-in-a-row against Irish opposition.
Sean Everitt's side have won three of their last four URC games against Connacht.
The Scots, beaten by Bath in the Challenge Cup semi-finals last weekend, include Lions prop Pierre Schoeman in their team this evening.
"We're pushing hard for a play-off spot, and with only two games left, every point matters," said Everitt, whose side are in tenth on 39 points, two behind eight-place Benetton ahead of round 17.
"We were disappointed with the result against Bath, but the performance had some real positives that we need to build on.
"It's vital that we learn from that game and maintain our upward trajectory.
"Connacht are always a tough team to face at home; they're passionate and play with a lot of energy in front of their own crowd.
"But we can take a lot of confidence from our European run and our recent URC form into this match. We know what we're capable of when we play to our potential."
Connacht: Santiago Cordero; Shayne Bolton, Hugh Gavin, Bundee Aki, Finn Treacy; JJ Hanrahan, Ben Murphy; Denis Buckley, Dave Heffernan, Finlay Bealham; Josh Murphy, Darragh Murray; Cian Prendergast (capt), Conor Oliver, . Sean Jansen.
Replacements: Dylan Tierney-Martin, Peter Dooley, Jack Aungier, Oisín Dowling, Paul Boyle, Caolin Blade, Cathal Forde, David Hawkshaw.
Edinburgh: Wes Goosen; Darcy Graham, Matt Currie, Mosese Tuipulotu, Jack Brown; Ross Thompson, Ali Price; Pierre Schoeman, Ewan Ashman, D'arcy Rae; Marshall Sykes, Sam Skinner; Ben Muncaster, Hamish Watson, Magnus Bradbury (capt).
Replacements: Paddy Harrison, Boan Venter, Javan Sebastian, Glen Young, Liam McConnell, Charlie Shiel, Ben Healy, James Lang.
Referee: Ben Breakspear (WRU)
