Cardiff have been in negotiations with the player for most of the week but it is thought that Stoke have outbid them in the last 24 hours.
The 21-year-old is available on a season-long loan, with parent club Benfica hoping the striker can continue his development with a season of regular football in the Premier League.
Stoke are said to have offered in the region of £860,000 to take the Portuguese international for the season.
Oliveira spent last season at Deportivo la Coruna where he scored four goals in 30 appearances, which you can view in the video above.
Stoke City set off for their tour of the USA this morning from Clayton Wood so it is thought that Oliveira would join up with the squad on their pre-season tour.
Brek Shea was thought to be linking up with the squad in America after last night's game for the USA against El Salvador, but USA won 5-1, so Shea will stay with the squad as they progress to the final.
Striker Kenwyne Jones has joined back up with the Stoke squad after Trinidad & Tobago were eliminated from the CONCACAF Gold Cup by Mexico in which the Stoke forward captained his team.
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