The Brazilian has been out since suffering a serious knee injury on New Year’s Day and Smith has confirmed he is still several months away from completing his recovery.
Villa have already smashed their transfer record with the £28million signing of Ollie Watkins but with Mbwana Samatta potentially heading for the exit door, they remain light on options at centre-forward.
Bournemouth’s Josh King and Celtic’s Odsonne Edouard are potential targets, while winger Bertrand Traore is close to joining in a £19m move from Lyon.
Talks are continuing with Werder Bremen over a deal for Kosovo international Milot Rashica.
Wesley, who joined Villa in June 2019 for what was then a club record £21m fee from Club Brugge, scored five Premier League goals before his maiden campaign in English football was cut short by an injury suffered in a 2-1 win at Burnley.
Smith said: “We believed it was going to be a 12-month injury and nothing has told us otherwise yet.
“The swelling has gone down on his knee now but it was quite a bad injury he suffered.
“He is back now with us but is not back training in any shape or form.
“He is getting full range into it and hopefully he will be back as soon as possible.”
Burkina Faso international Traore is expected to complete his move in the next 48 hours but his arrival will not mean the end of Villa’s business.
“We are still trying to bring a couple more players in, we think we are still light in a couple of areas,” said Smith.
“But we think it has been a very good window so far with what we have had to do. We have brought in good quality so far and are looking to add to that.”