Dempsey is leaving for Japan and Fagerson described his Scotland teammate as "irreplaceable".
With Jamie Ritchie expected to join Glasgow and Dempsey and Sione Vailanu departing, there has been speculation that Fagerson could switch from blindside flanker to No 8. The 27-year-old, who played much of his early career in that position, says the possibility has been discussed.
Asked if it's been spoken about, Fagerson replied: "Yeah, a little bit. Obviously, we've got Ruwald [van der Merwe] coming in, who I think he plays across the back-row, and Macenzzie Duncan this year as well who has played eight, he's played across the back row. But I think, obviously, losing Sione [Vailanu] and Jack, he's a bit of an irreplaceable character and player.
"We've had discussions, obviously. I've played eight a lot at the start of my career and really enjoyed it. I sort of felt like my carrying came into its own then.
"When Jack came, I probably had to learn a bit of how to play six. Maybe I wasn't as much of a line-out forward before then. So yeah, we've had conversations about it, but it's not about trying to replicate what Jack does because I don't think I would do it justice."
Asked if he'd relish the chance to play at number eight, Fagerson continued: "Yeah, massively. It's an incredible place to play. You're in the backfield more, you're carrying off of set-piece. It takes a couple of weeks to get back into the groove of your running lines and the role you have in the team, and a lot of the pressure is on you for the front foot ball. So yeah, that's a challenge I'd love to play more at."
Ritchie's move to Scotstoun has yet to be officially announced, with Glasgow focused on their URC campaign.
Asked if he has spoken to his Scotland teammate about the move, Fagerson said: "There's been a few rumours floating around. But, yeah, he's obviously had a tough run towards the end of the season at Perpignan with his injuries and stuff. So yeah, we keep tabs on him now and again. But hopefully he'll be fit for the summer."