The Dutch winger offered himself to his former club during the summer but was told that they only had funds for signing a forward
The midfielder attempted to contact the Rotterdam club after his Real Madrid contract was not renewed in the close season. However, a move did not work out.
"I phoned Royston to speak to him because he tried to contact us," Koeman told Voetbal International.
"I explained that we have enough players in the [his] positions and that we wanted to spend little money, and only on a striker."
Drenthe, who spent time on loan at Everton and Hercules following his transfer to the Bernabeu, began his career in the Eredivisie and spent two seasons with Feyenoord between 2005 and 2007.