The Argentine full-back joined the Dutch giants from Independiente in January 2018 and quickly cemented his place in the first-team.
The 27-year-old's exploits for club and country have caught the attention of several top teams. While Atletico Madrid reportedly saw a deal for him collapse last summer, Barcelona are said to be eager to land him this time around.
After 99 appearances for Ajax, Tagliafico has hinted that he has had enough of playing in the Eredivisie and wants to leave to play in a more challenging league.
“It was always my goal to play in the best competitions, at a top club,” Tagliafico said in an interview with radio station Continental.
“Ajax is a great club, but the Eredivisie is not a great competition. You must always have dreams. The preparations will start in August for around two months. But whether or not I'll leave... It's all uncertain.”
It has been reported in Spain that Barcelona are eyeing a summer bid for him as they look to replace Junior Firpo, who has failed to break into Quique Setien’s team since joining from Real Betis last summer.
Mundo Deportivo claimed last month that the Spanish giants have already held several talks with Tagliafico’s agent, while the player is said to be eager to reunite with Frenkie de Jong and Argentina co-star Lionel Messi.
But Tagliafico says he has not heard anything definitive from the Catalan giants and is keeping his feet on the ground
“I'm trying to think about my condition, to stay fit as possible in case I go to another club,” he added.
“I'm standing on the sidelines. Maybe I'm on [Barcelona’s] list, but there is nothing concrete.
“You must stay calm. I'm also trying to stay calm. If something happens then I'll talk with my agent.”
Tagliafico, who has won the Eredivisie and Dutch Cup during his time in Amsterdam, still has two years left on his contract with the club.