Gregor, who will take over as Scotland coach next June, is convinced the Warriors can reclaim the championship that they won in the 2014-15 season.
Speaking at the launch of the new PRO12 season, Gregor said: "The squad are capable of it. Definitely. They're capable of going far in Europe. But it's going to be very tough.
"I see this PRO12 being more competitive than the last two, which were already pretty competitive, with four or five teams pushing right to the wire. I can see seven or eight teams this year in the mix. We've all got our players from the beginning of the season, so you should teams really competitive right at the beginning.
"We'll have to be - we're playing the best teams right at the beginning. So it will be challenging, but with the group that we have, and their mindset and the effort they put in in in training does get its rewards. We've seen that in pre-season. So we want to build on that over the next few weeks.
"I genuinely mean this - any one of seven or eight teams could win. I think Cardiff are one of the best teams just now, one of the fastest improving teams and made some very good signings. Edinburgh were second in the league when they beat us for the second time in January, and they've got some key players back from injury.
"We'll know where we are probably after the first four games, because they'revery tough. We're playing the three semi-finalists and Cardiff in our first four games, so thank you PRO12."