Barely a week goes by without the Frenchman being asked whether progress has been made on persuading top scorer Walcott to stay at Emirates Stadium.
Walcott, who has hit eight Premier League goals this campaign, is out of contract at the end of the season,
"Discussions progress smoothly but slowly. We are on a good road but in this situation, as long as nothing is signed, you are cautious," Wenger told a news conference on Friday.
"But I am optimistic we will get to a happy conclusion. I was optimistic last week, but I am a bit more optimistic this week."
Walcott has made no secret of his desire to switch from the wing to play in the centre-forward role and has revelled in that position in recent games, including netting a dazzling hat-trick in the 7-3 win over Newcastle United in late December.
Wenger said any new deal would not revolve around Walcott being assured of playing as a central striker, although he did envisage him getting more time in that role.
"No, it is not linked with that," he said. "I believe that Theo can have a preference maybe to play through the middle but first of all he never made a condition of that to extend his contract, because certainly I would not accept it.
"Secondly he was always happier when he plays, whether it is on the flank or through the middle. That has no influence at all. But I see him playing more up front, yes."
Arsenal host second-placed Manchester City on Sunday with striker Olivier Giroud rated as "50/50" to play by Wenger after suffering a cut knee in the FA Cup tie with Swansea last weekend.
Sixth-placed Arsenal are unbeaten in five league games but Wenger said his side needed "another positive result in a big game" to maintain pursuit of the clubs above them.
"We know this a vital period for us," he said. "We are on a positive run. We still lack a bit of confidence in some situations and I feel our team will be very dangerous if we have full confidence.
"We are not far from it but we need another positive result in a big game to be completely confident and believe in our ability to come back."
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
‘Ruben Amorim could have waited for Real Madrid and had a better chance to be successful – to have joined Manchester United, he must be convinced in his own ability’ Former Old Trafford coach’s verdict on new boss
