The 21-year-old Frenchman is reportedly a transfer target for Serie A club Napoli after finding the net 40 times in all competitions since making his Hoops bow in 2017.
Six of those goals have come this season, helping him win the Ladbrokes Premiership Player of the Month award for August on Tuesday.
But Edouard brushed off the speculation and insisted he needs to focus on Celtic.
Speaking via a translator, Edouard said: "I actually didn't know about this [the report] and it doesn't really matter. At the moment I'm a Celtic player.
"I've got a season to play, I've got a long contract, I'm really happy with the way I'm playing, the set-up here and I'm really happy to play with my friends for the team.
"The main thing at the moment is I'm a Celtic player and I'm happy to be a Celtic player.
"I've still got a lot to prove with Celtic, as part of the Celtic team. There's a long season ahead of us, we need to concentrate on that.
"The key is I've got to prove myself here first."
Celtic are gearing up for their first Europa League group clash, an away trip to Rennes on Thursday.
Edouard, who enjoyed a loan spell with Toulouse in the 2016-17 Ligue 1 campaign before joining Celtic from Paris St Germain, knows all about Celtic's next opponents.
Rennes have made a bright start to the season, beating PSG 2-1 last month as they won their opening three league games.
They have picked up just one point from their last two matches since that winning run, but Edouard expects a tough test at Roazhon Park.
He added: "I know the team quite well because I watch Ligue 1 regularly.
"I know it's going to be a very difficult game, so it's for us to go there, make sure we get a result and come back with that."
Like Rennes, Celtic have started their league campaign well, winning all of their five Premiership matches to date, with Edouard scoring in three of those games.
And Edouard thinks both he and Celtic must keep up the good work.
He said: "The important thing is that we continue in the same vein really.
"I've been working really hard in training, so that's paid off. But the important thing is this is a team result.
"I'm playing well because the team is playing well. Yes, I hope this is going to continue, but it's not just about me, it's the whole team supporting me."