Narsingh, 21, and Assaidi, 23, both travelled to London on Monday to tour Fulham's training facilities and ground.
They were accompanied by their agent Mino Raiola, who began talks with the club over personal terms as Fulham look to strike a double deal.
Heerenveen confirmed they gave both players permission to travel to England.
"We have given Mino Raiola and the players the space to talk," Heerenveen technical director Johan Hansma told De Telegraaf.
"Narsingh and Assaidi had to have a good feeling with a club. It doesn't make any sense if we reach an agreement with a club and the players won't want to go there. To succeed in a transfer there are three sides needed."
Narsingh, who has been named in Holland's preliminary squad for Euro 2012, and Assaidi - a Morocco international - both have one year left on their current deals at the Abe Lenstra.
Ajax and PSV Eindhoven are also very keen on Narsingh and are also due to hold talks this week.
Meanwhile, reports in Holland also claim that Fulham are keen on FC Twente ace Nacer Chadli.
Twente chairman Joop Munsterman denied claims that he had given permission to Chadli's agent Daniel Evrard to talk with Fulham or any club.
Munsterman told Voetbal International: "I have become a little bit nervous of Evrard. He always drops a couple of names of clubs, but they never contact us. We aren't talking with any club right now."
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