The Scottish Premiership side have failed to make an impression in Europe for the last two seasons.
The Northern Irishman has been appointed as Ronny Deila's successor, after the Norwegian's inability to lead the Hoops on any kind of European run led to his tenure coming in for severe scrutiny before his recent departure.
And Gemmell - who famously scored the equaliser in their 1967 European Cup final victory - explained that the Bhoys should be looking to put themselves alongside the very best that the continent has to offer, and, perhaps in a warning to Rodgers, suggested that their failure to do so under Deila was the catalyst for his exit.
"Europe is where a club of Celtic's stature should be judged. That's where they have to make an impact," he told The Scottish Sun.
"They should be up there with Real Madrid, Barcelona, Bayern Munich and so on. That's the company they should be mixing in.
"But, of course, it is Europe where we have failed over the past couple of seasons and I think that ultimately led to Ronny Deila leaving at the end of the season."
Though Gemmell wants to see the Hoops competing in Europe, many who watched the side last season may struggle to believe that Rodgers has a squad available to him that is capable of competing in the Champions League while also continuing their run of league victories.
However, Rodgers proved during his time with Liverpool that he has the potential to take a promising side and, with a few additions, turn them into something special.
And with Celtic facing a simpler task than the Reds did when it comes to remaining near the summit of their respective league, it may be easier for the new boss to keep his best players at Parkhead, and thus, build towards re-establishing themselves in Europe.