The 24-year-old France international has been attracting attention from across Europe and has been linked with a move to the Premier League.
One club reportedly showing an interest is Arsenal, with the Gunners taking on Lyon in the Emirates Cup on Saturday.
Speaking ahead of the match, Fournier insisted Lacazette is happy at the Stade de Gerland and will be an important part of a Lyon squad which will be looking for success in all competitions having finished second to Paris Saint-Germain in Ligue 1 last year.
When asked where he saw Lacazette playing this season, Fournier said: “Olympique Lyonnais.
“I haven’t got much to say. He has said he wants to stay with us.
“Of course some clubs are going to be attracted to the sort of player he is but he is under contract at Lyon and with all of the different competitions we have this season with the Champions League and the domestic French cups, we obviously want to keep him at the club.”
Their second-place finish means Lyon will meet double winners PSG in the Trophee des Champions next weekend, with Fournier seeing the Emirates Cup as a great way to prepare for their first trophy tilt of the campaign.
“It is another exciting test for us,” he said of his side’s participation in the friendly tournament.
“It is going to allow us to give additional playing time to the entire squad. We are going to have 90 minutes in our legs before the Trophee des Champions final against Paris Saint-Germain.
“We think it is an important trophy, myself, the staff and the players – it’s a competition we will take seriously, that is why we are preparing seriously for it.
“These matches will allow us to get up and running so we can be at our best in that competition.”
Fournier did not single out a particular threat amongst the Arsenal ranks but did hail manager Arsene Wenger as the top boss in world football.
“For me – he is the best,” he said of compatriot Wenger.
“I think Arsenal’s main strength is their team play. They are led by some real top players form the international stage, the main concern is Arsenal’s team play.”
Having played Arsenal on Saturday, Lyon will face Primera Division outfit Villarreal on Sunday, with the Gunners facing Wolfsburg.
Travel and weather woes meant neither Wolfsburg coach Dieter Hecking and Villarreal counterpart Marcelino Tora were able to talk to the press ahead of the tournament.
Their two sides will kick-off the competition on Saturday afternoon, with Arsenal looking to win their own tournament for the first time since 2010 – when Lyon finished as runners-up in their last appearance.