The England international is free to leave the club when his contract expires in the summer and has yet to agree terms on a new deal.
However, Wenger remains hopeful that the 23-year-old will still be at the Emirates Stadium next season.
"[Talks] are going on but there is no news about that," said Wenger.
"My determination has always been the same and that is to extend his contract. Other clubs are interested but the determination is the same."
"The good news is he has had his first run [on Tuesday] and should be back shortly."
Serie A champions Juventus, Premier League champions Manchester City and Liverpool have all been linked with a move for Walcott.