The 24-year-old midfielder has attracted attention from a number of Premier League clubs, following a series of impressive performances in the Dutch Eredivisie last season.
Tadic scored 13 league goals in his debut campaign at De Grolsch Veste, as Twente finished sixth in the table, one place above his former club Groningen.
However, with Ajax, PSV Eindhoven, Feyenoord, Vitesse and FC Utrecht beating the club to a place in the Champions League or Europa League, Twente will not play in European competition in 2013/14.
Gunners boss Arsene Wenger has been credited with an interest in bringing Tadic to the Emirates Stadium, and the opportunity to test himself in Europe's elite club competition will be a huge pull for the player.
Everton are also believed to be monitoring the Serbia international's situation, but Arsenal would likely be the more favourable option, given their inclusion in the Champions League.
"I feel good at FC Twente, but I am a professional and if a good offer for me and the club arrives then we have to go to look at it," Tadic admitted in an interview with De Telegraaf.
"There is a lot of interest, but so far I have left everything to my manager. If there is something concrete, he will inform me."