Arnautovic has scored five goals in 15 Premier League appearances this season, including his brace against Manchester City on Dec. 5, while Pieters has featured in all 16 of Stoke's league games this season.
"Yes, they are contracts we are working on at the moment," Coates told the British media.
"We are always aware of these things, of where we want to go with them, and are trying to make sure we get things done in good time."
The Potters are 11th in the table, with Pieters part of a defence that has kept five clean sheets in their last six league games.
(Reporting by Simon Jennings in Bengaluru)
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