Reports in Friday's newspapers suggested Real were set to make a £16million bid for the 23-year-old within the next 48 hours and the Spanish club's president Ramon Calderon has previously stated his desire to take Robben to the Bernabeu.
But Kenyon has played down the rumours and insists he expects Robben to stay at Stamford Bridge, even though he is yet to sign a new deal with the club.
Speaking at a press conference in Hong Kong to launch a new merchandising deal, Kenyon said: "Arjen is very happy, he's just got married and he wants to demonstrate and prove what a great player he is and still believes the Premier League is the best opportunity.
"I'm confident he'll be there next season."
Kenyon also poured cold water on rumours Chelsea were lining up a bid for Lyon midfielder Florent Malouda and insisted the club were planning no big-money signings this summer.
"By Chelsea standards it's been very quiet," he added. "That's probably the headline...both in terms of names and in terms of big spending.
"We've had three or four so-called free transfers."