The Rotterdam club's sporting director has admitted that he would love to see the attacker return to De Kuip, but conceded that a summer switch might not be feasible
The Netherlands international has been struggling to find his best form in the 2011-12 campaign, and recently revealed that he could opt to leave Anfield if he is not given regular first team action at Liverpool.
"I would love to welcome Dirk at Feyenoord as soon as possible. He fits in here more than anybody else," Van Geel was quoted as saying by NUsport.
"He is more than welcome at the club. However, I do not think that it's realistic to believe that he could return this summer."
Rob Jansen, the player's agent, added that Kuyt is keen to return to Feyenoord at some point, but stressed that he hasn't made a decision yet about his immediate future.
"Feyenoord know that Dirk will join them once he returns to Netherlands. But when? It's impossible to answer that question," Jansen stated.
"We are just waiting to see what happens at Liverpool now and what's coming his way. We will make a decision on his future after that."
Kuyt has a contract with the Merseysiders until the summer of 2013.