The ex-Espanyol coach, 45, met Barca president Josep Maria Bartomeu last week as speculation increased that he might take over from Luis Enrique.
However, BBC Sport understands that he is not under consideration for the job.
"I'm an Espanyol supporter - I think then I don't need to speak too much," the Argentine said, highlighting the rivalry with city neighbours Barcelona.
He also played 216 games for Espanyol.
At Thursday's news conference, Pochettino said: "It is like one day if [Spurs chairman] Daniel Levy sacks me in a few years, it would be impossible to manage Arsenal."
Reports say Spurs were aware of the Argentine's meeting with the Barcelona president.
Barca assistant manager Juan Carlos Unzue is favourite with the bookmakers to take over from the departing Enrique, with Athletic Bilbao coach Ernesto Valverde also thought to be in contention.
Tottenham manager Mauricio Pochettino has suggested it would be "impossible" to ever manage Barcelona.