The Eredivisie side is open to selling the defender before his contract expires next year but is determined to hold on to midfielder Jordy Clasie.
The young defender was one of the revelations of the World Cup and has been monitored closely by Lazio before the start of the 2014-15 campaign, while Manchester United has also been linked with a bid as Louis van Gaal continues his rebuilding work at the club.
With De Vrij's contract set to expire within a year, Feyenoord is seemingly willing to negotiate a sale this summer - provided a strong enough bid emerges.
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"Stefan is a player who came through our youth academy and played in the first team for five years," Van Geel told De Telegraaf. "He played an amazing World Cup and his contract is due to expire in one year.
"If the right club comes along and puts in a good offer, we will definitely look at it."
The 22-year-old has made over 150 official appearances for Feyenoord since breaking into the first team in 2009-10 and has been capped at senior level 19 times, scoring once in the progress.
However, Feyenoord is determined to hold on to Jordy Clasie for one more season, regardless of reported interest from Fiorentina and Porto.
"Jordy is very happy at Feyenoord and we have no intention of selling him. A transfer is not really a must for him. I don't expect too much to happen around him," Van Geel said of the midfielder.
"We are willing to go the extra mile to hold on to him and the rest of the team."
Feyenoord has already lost Graziano Pelle to Southampton, while Daryl Janmaat (Newcastle United) and Bruno Martins Indi (Porto) are both expected to complete moves away from the Rotterdam giant in the coming days.