The 27-year-old France striker is currently on loan at Newcastle from QPR, and the Magpies are desperate to complete a permanent deal at the end of the season.
However, the former Marseille frontman has ambitions to perform at the highest possible level one day.
He told France Football: "Nowadays, without being pretentious, I might be able to play for a bigger club, a top-five European club.
"I do not know... Yes, I will be part of the European top five, or I will be part of a very large club. I'm sure of what I can do. I can still be much better."
Remy has scored 13 Barclays Premier League goals for Newcastle so far this season, including one in each of the two games in which he has appeared since returning from a three-match ban.
He joined the Magpies on a season-long loan deal in August last year following QPR's relegation to the Sky Bet Championship.
However, he might have arrived at St James' Park some seven months earlier with Alan Pardew having tried to sign him before he headed for Loftus Road instead.
Remy eventually joined the Tyneside club with an allegation of rape hanging over his head.
The case against he and two other men was dropped last month, but Remy, who denied the accusation, admits the uncertainty put off many potential suitors and, in the circumstances, he is grateful for Newcastle's support.
He said: "At QPR, during the first half of 2013, I had a good six months. But this story cooled a lot of clubs.
"I had the chance to come to Newcastle - a great club that I thank. They supported me a lot in this case. The verdict was a great weight lifted."