The France international found himself relegated to the bench in the opening few weeks of the season after being usurped by January signing Pierre-Emerick Aubameyang, leading to suggestions that he could move on.
Lacazette took full advantage of his first start of the season at the weekend, however, netting a late winner for the Gunners in their 3-2 win over Cardiff City.
With the transfer window now closed until the New Year, the 27-year-old has suggested that it was never his intention to quit the Emirates Stadium.
"I don't know who said this stuff, but I am at one of the best clubs in London and I am happy at Arsenal," he is quoted as saying by Sport360.
"It's always going to be hard to be in the first XI at a club like this, but I always keep fighting and working. I won't play every week just because of one game. Every day I have to work and show the coach I work well and I deserve my place."
Lacazette has now been directly involved in seven goals in his past five Premier League starts.