Walcott was in devastating form on Sunday, netting a top quality hat-trick in the Gunners' 4-1 victory over West Bromich Albion to end the season on a high.
However, the 2014/15 campaign has not provided too many bright spots for the England international, who has been stymied by injury and a failure to cement his place in Wenger's starting line-up.
Reports have suggested that efforts to extend Walcott's current contract, which expires in 2016, have hit a roadblock, with the 26-year-old and the club to find common ground.
At the same time there have been rumours that Walcott will look to leave the Gunners in order to get consistent game-time and to play in his preferred role down the middle, with Wenger more often than not selecting the former Southampton man out wide.
"Without his hat-trick or with his hat-trick, we want him to stay. We are in negotiations and we have started to speak with his agent," Wenger told the club's official website of Walcott.
"We did that before he scored his hat-trick. Last time he got injured he was playing centre forward in a very convincing game against Tottenham Hotspur in January.
"He got injured and was out for a year. On that day he was injured playing up front."
Walcott joined Arsenal in a big-money move from the Saints in 2006, and made his debut for the club aged just 17.