Manchester United boss Louis van Gaal has said that Darren Fletcher's proposed move to West Ham is off.
Hull boss Steve Bruce says his side's 3-0 defeat to Newcastle may have jeopardised his chances of strengthening his squad.
The former Holland defender's current deal expires at the end of the season but technical director Martin van Geel is hoping his stay at De Kuip can be extended.
Koeman guided Feyenoord to a second-placed finish last season and they are currently fifth in the Eredivisie, nine points behind leaders PSV Eindhoven.
Van Geel told Voetbal International: "We would love to (extend his deal).
"That we were second last year and now, even though we had to let some important players go, are fifth is clearly largely due to Ronald Koeman.
"We'll talk during the winter.
"We are very happy and I hope Ronald is too.
"As a coach, he has the necessary experience of highs and lows, and perhaps he cherishes the situation in which he can work."