The Stoke midfielder thinks his teammate can get the better of the league leaders' high-profile hitman.
Costa is one of the toughest strikers to face in the Premier League this season - and not just because he shares the lead in the goalscoring charts with 19 goals.
The Chelsea hitman has a reputation for getting under the skin of his opponents in several different ways but Adam thinks Shawcross will be a match for his dangerous opponent.
The midfielder is quoted in the Stoke Sentinel, saying: "He's a top-class, powerful striker who's similar to when (Didier) Drogba first came over.
"He's a strong centre-forward and a good player, but Ryan knows how to play against him and did well the last time he played against him.
"But it's not just Costa we have to watch. There's also (Cesc) Fabregas, (Eden) Hazard and a lot of other good players."
Shawcross also has a reputation for being one of the most awkward and physical centre-backs a forward can face in the league, so the battle between the duo on Saturday evening is likely to prove key in the outcome of this match.
But as Adam has pointed out, even without Costa at the top of his game or nullified by Stoke, there are other threats in the Chelsea side, even if they themselves haven't been firing on all cylinders.
It's rare you see a side leave Stamford Bridge with something to show for their efforts - though sides will have started fancying their chances lately given the lethargic displays from Jose Mourinho's side, but the Potters are going to have to be at their best to get something off Chelsea this time.