Walcott's current deal expires at the end of the season and he has so far refused Arsenal's offer to renew his contract, sparking speculation that the England winger could be ready to quit the Emirates Stadium.
The 23-year-old, who is allowed to speak to foreign clubs about agreeing a pre-contract transfer from January, underlined his value to Arsenal as he came off the bench to inspire Saturday's 3-1 win at West Ham with a goal and an assist.
But Walcott, also a target for Liverpool and Chelsea, has started just one league game this season, while making a further five appearances from the bench.
That kind of involvement is unlikely to persuade Walcott to stay, but Wenger believes he is still willing to commit to Arsenal.
Asked if he thought Walcott would re-sign, he said: "I think so. But I cannot tell you what he tells me.
"We are always in touch. He has character. He keeps focused and he wants to show he is 100 per cent professional and I have a big respect for that attitude."
Walcott has called for Wenger to give him a chance through the middle and the Frenchman admits he could yet be given that opportunity.
"Theo's game is based on movement off the ball, timing and finishing. He can play wide, he can play centre," he said.
"Basically it is not so important. He has improved a lot in his finishing. Even if he plays wide or centre he gets in positions where he can score."