The Brazilian striker is scheduled to take part in non-contact group training at Bodymoor Heath as nears the end of his long recovery from a serious knee injury.
Villa’s plan is for Wesley to resume full contact training in mid-January, with the hope he may then be ready for a return to action toward the end of the month.
The 24-year-old, who joined in a then club record £21million deal from Club Brugge in 2019, has not featured since suffering the injury in a Premier League fixture at Burnley on New Year’s Day 2020.
Smith said: “Wesley will be joining in with the group this week on a non-contact basis, just to get him in among the players.
“We will have more of an idea when he starts full contact training, probably in two weeks. He is getting a lot closer now, which is pleasing.”
Wesley had scored five goals in 21 Premier League appearances before his debut season in English football was cruelly cut short.
His progress over the coming weeks will determine how fiercely Villa pursue attacking targets during the January transfer window.
Smith has suggested a pragmatic approach to the month for a club which spent £80m on five signings during the previous window.
Recent performances have helped convince the boss there is depth to his squad, which will be further boosted by the returns of Ross Barkley and Trezeguet from hamstring injuries.
Smith said: “We believe we have good depth in the squad, with four or five players coming back from injury, which will be a big boost to us in January with the number of games we have.
“We are always looking for good value opportunities. We will never turn our noses up. But they have to be there, if we are to move.”