The United States international suffered a hamstring injury in his country's opening World Cup fixture with Ghana in June.
However, he made his comeback as a second-half substitute in Sunderland's 2-0 friendly victory over Udinese on Saturday.
Sunderland head coach Poyet believes the 24-year-old could now be ready for the visit to The Hawthorns after a full week's training.
"Jozy is coming along well," Poyet told the club's official website.
"We were thinking he could feature for 45 to 30 minutes [against Udinese], the idea was to get him to play a part in case we need him in any games.
"I'm sure he will work a little bit more this week and a full week of proper training will help him be part of the squad for [Saturday]."
Altidore scored just once in 31 Premier League appearances last season.
