Last season they twice defeated Irish provinces, Munster and Ulster, on their way to the semi-finals and Irishman Mark McCall is hoping victory in Galway can propel his team towards further success.
Lions duo Owen Farrell and Mako Vunipola are both available, while England wing Chris Ashton looks to be heading back to form, although Brad Barritt is out of action with a foot problem.
However, head coach McCall is only too aware of the challenge Saracens face at the Sportsground on the opening weekend of action in Pool 3.
"I know from experience that we have one of the trickiest starts you could ask for in Galway," said McCall.
"That's not just opinion, the facts speak for themselves. Over the last three years, Connacht have beaten Biarritz and Harlequins in Galway so unless you take your A-game and have the right mind-set, you will get the same result those teams did.
"There is always a great crowd in Galway, they have good players and a top coach in Pat Lam and have recruited really well, that's why they get the scalps they have."
Connacht have lost their last three games in the RaboDirect PRO12 but there were plenty of signs in their last home game, when they scored 26 points past the Ospreys, that the likes of new signings Jake Heenan, youngster Kieran Marmion and Super XV winning captain Craig Clarke are starting to gel.
Connacht have also received a boost with the return of their most-capped player, Michael Swift, to fitness after missing the trip to Treviso through injury but centre Eoin Griffin and props Nathan White and Ronan Loughney are out.