Gibson moved to Glasgow after four seasons and 92 appearances at Welford Road, playing for the last time in the Tigers' Heineken Cup final defeat to London Wasps last season.
And he believes the Warriors have the potential to surprise their more illustrious Pool Four rivals Saracens and Biarritz in a group which also includes Italy's Viadana.
"I think for Glasgow we could be a bit of a bogey team for the more-vaunted sides in our pool, which are Biarritz and Saracens," Gibson said.
"They are probably the two favourites to take the pool, but we're certainly going to be competitive against those sides and we can certainly cause an upset on our day.
"I don't think those sides are going to have it their own way."
Victory over Saracens or Biarritz would be a triumph for Glasgow and Gibson, who is the backs coach at Firhill Arena as well as the team's leading inside centre, will be integral to the chances of success.
His experience, which includes 19 caps for the All Blacks as well as 78 Super 12 games for the Canterbury Crusaders in his native New Zealand, will be crucial for the Warriors.
The 32-year-old was involved in some of the great triumphs for Canterbury - he won four Super 12 tournaments, five Ranfurly Shields and two National Provincial Championships.
He played at a time when Canterbury and New Zealand had an array of options all along the three-quarter line.
Gibson's versatility earned him a place at the 1999 World Cup, but it was perhaps one of the reasons why he failed to reach 20 international caps and opted for a move to Europe.