The 21-year-old midfielder is widely regarded as one of the hottest prospects in the Eredivisie at the moment, and has been likened in playing style to Barcelona maestro Xavi Hernandez.
Gunners boss Arsene Wenger has been credited with an interest in bringing Clasie to the Emirates Stadium, while Andre Villas-Boas is believed to have identified the Dutchman as a long-term replacement for Scott Parker at White Hart Lane.
However, both Spurs and Arsenal will face competition from Premier League leaders Manchester United, with Sir Alex Ferguson also weighing up a bid for the £6.5million-rated midfielder.
The Red Devils manager wants to strengthen his Old Trafford options in the middle of the park ahead of the 2013/14 campaign, and according to Spanish website fichajes.com, Clasie is the man on the 71-year-old Scot's summer wish-list.
Clasie has impressed in 34 appearances for Feyenoord this season, scoring two goals and making numerous assists, catching the eye of a number of top European clubs, including Serie 'A side Fiorentina, who are thought to be the only club to make a firm offer for the player's services.
Last month, Feyenoord's technical director Martin Van Geel was quoted by the Daily Mail: "We do not need to sell him, nor do we particularly want to, but we have to think of the player's ambitions and evaluate the offers from other clubs.
"There is an offer from Fiorentina, but we'll only discuss it at the end of the season. Right now the players must focus only on Feyenoord."