Lacazette has started the new season well for Arsenal and his goal against West Ham in the 2-1 win on Saturday night was his second in as many games.
Arteta praised the Frenchman in the wake of the victory over the Hammers, and hinted he wants him to stay, but the Spaniard also confessed no talks are underway over a new deal yet.
“At the moment we haven't started any negotiations. We have a lot of things still to do in this market," said Arteta.
“He is a player I am really happy with. I think we showed him a lot of faith since I arrived here. But we cannot stop any speculation.
“We know that any player that is under two years contract is always going to be talked about."
Arsenal were not at their best against West Ham, but they managed to grind it out to claim all three points and maintain their perfect start to the season.
“I'm thrilled with the three points. I said before the game how difficult it would be with the way they play," said Arteta.
“We made it even more difficult in the first 15 minutes with the amount of balls we gave away and the open spaces we gave them to run into.
“I'm glad we found the right moment and kept competing and believing, with good momentum in the last 25 minutes.
“We created many other situations. But we gave too many opportunities to the opponent in the final third. There are still a lot of things we need to get better at.
“Eddie can do that every week. He's hungry and has a great quality to score goals."