While the capital side have had a difficult campaign, Connacht are flying high in second place behind Guinness Pro14 conference B leaders Munster.
Cockerill admits his team will have to be at their maximum to upset Andy Friend’s Westerners.
He said: “Galway is a tough hunting ground for travelling teams and they’ve performed very well this season and deserve their place as the current runner-up in our conference.
“Andy Friend has them well coached so it will take an excellent performance from us to come away with the points this weekend.”
Cockerill has made two changes to the XV he named for last weekend’s postponed match against Benetton.
No 8 Bill Mata – unavailable for selection last weekend through injury – makes a timely return in place of Nick Haining, who has been named on the bench for Scotland against Ireland along with hooker David Cherry, which sees Mike Willemse promoted from the bench.
Prop Simon Berghan and stand-off Jaco van der Walt have also been recalled by the national team, with the former also among the substitutes against Ireland.
Berghan’s place on the bench is taken by Watsonians tighthead Angus Williams, who is one of three potential debutants named, with hooker Sam Kitchen and stand-off Charlie Savala also waiting in the wings.
Injury kept Van der Walt out of contention last weekend, so his international recall ensures the reinstatement of 20-year-old stand-off Nathan Chamberlain alongside scrum-half Charlie Shiel.
The young duo will steer the reselected back division of George Taylor and James Johnstone in midfield and a back-three trio of Eroni Sau, Jack Blain (wings) and co-captain and full-back Damien Hoyland.
Props Pierre Schoeman (co-captain) and Lee-Roy Atalifo are renamed alongside Willemse in the front-row, Magnus Bradbury partners Andrew Davidson at lock, while Ally Miller and Luke Crosbie return alongside Mata in the back-row.
Edinburgh: Damien Hoyland (co-captain); Jack Blain, James Johnstone, George Taylor, Eroni Sau; Nathan Chamberlain, Charlie Shiel; Pierre Schoeman (co-captain), Mike Willemse, Lee-Roy Atalifo, Magnus Bradbury, Andrew Davidson, Luke Crosbie, Ally Miller, Bill Mata.
Replacements: Sam Kitchen, Boan Venter, Angus Williams, Jamie Hodgson, Mesu Kunavula, Henry Pyrgos, Charlie Savala, Mark Bennett.