The pair are reported to have eaten together at a restaurant in the Catalan capital, where Pochettino has a home, as Bartomeu assesses who should succeed Luis Enrique as coach at the end of the season.
Standard Sport understands Spurs were aware the meeting would happen, as they say Pochettino, 45, and Bartomeu, 54, are friends.
As he nearly always does, Pochettino has decided to spend some time in Barcelona during the international break.
When asked about the vacancy at Barcelona earlier this month, Pochettino did little to distance himself from speculation that he was on the club's list.
"I understand the football business very well but I can only say I am happy here," said Pochettino on March 3, when he was last asked about the Barcelona link.
Before Barcelona's remarkable 6-1 Champions League win over Paris St Germain recently, Enrique confirmed he would step down at the end of the campaign.
Since then, the favourites for the job have been named as follows: Enrique's assistant Juan Carlos Unzue, Athletic Bilbao coach Ernesto Valverde, and Sevilla coach Jorge Sampaoli.
Pochettino is a former player and coach of Espanyol, Barcelona's city rivals. He has suggested in the past that this would make it difficult for him to work for Barça.
"I am periquito," he said last September, referring to Espanyol's nickname. “The Espanyol supporters are different to the Barcelona supporters. For me, Espanyol supporters are better because I am Espanyol supporter. That creates a bit of a problem between us.
“Always it was special to beat Barcelona because it is my sporting enemy. I am from Argentina but I spent half my life in Barcelona and my two sons were born in Barcelona."
Pochettino has led Tottenham to second in the Premier League this season, and to the semi-finals of the FA Cup, on a smaller budget than those of the other clubs in the top six.
He signed a new five-year contract at Tottenham, worth about £5.5million annually, in May 2016.