The Dutch winger was quoted on Wednesday as being open to the prospect of securing a loan switch to former club Ajax during the January transfer window.
The 22-year-old is said to have grown disillusioned at a lack of opportunities at Anfield, with his World Cup aspirations weighing heavy on his mind.
Babel was awarded a starting berth by Rafa Benitez for Liverpool's opening game of the 2009/10 campaign at Tottenham, but has fallen down the pecking order since then.
Fellow Reds forward Kuyt understands his countryman's frustration, but he believes his international team-mate is prepared to fight for a place on Merseyside.
"He loves to play games for Liverpool and he will do everything in his power to come back," Kuyt told Sky Sports News.
"He is happy at Liverpool but every player wants to play and that is his only concern, before the World Cup, that he has to play games.
"I'm sure that he wants to play for Liverpool and that he wants to play in games as soon as possible.
"We have a big squad, with many players who can play in his position, so he has to work hard and I believe he is doing that at Liverpool and with the Dutch team."