The Scotstoun-based club have been drawn in Pool 4 for next season along with Northampton Saints, Ulster and Castres.
"I believe any team from that group can come through but every game is going to be tough," Gregor told BBC Scotland.
"Winning away from home will be hard but we have to win at least four games to get out of our pool and I believe we have the players to do that."
Gregor played for former European champions Northampton and also helped French outfit Castres reach the Heineken Cup semi-finals in 2002.
"I always keep an eye out for for the results of both teams and I'll be watching them even more carefully now," added the former Scotland and British & Irish Lions fly-half.
The new coach has been set high standards by managing director Nathan Bombrys.
"We've been able to bring in some top-quality talent, which is fantastic for the club," said Bombrys.
"We now expect to be performing consistently.
"Our minimum expectation is the league play-off semi-finals or quarter-final qualification in the Heineken Cup.
"We've been semi-finalists for two of the last three seasons."