The Spanish defender remains linked with a possible approach from Tottenham Hotspur.
"I don't know Bartra (well), I'm sure if he's at Barcelona it's because he's a good player, but we're not interested in him." Pinto da Costa explained, keen to end the rumours his club will be making a bid.
There were also suggestions FC Porto coach Julen Lopetegui, who worked with Bartra whilst he was Spain Under-21 manager, had specifically requested FC Porto make Barcelona an offer.
However, Da Costa simply contested: "Lopetegui is in Cancun on holiday until next week, and he said nothing about the player before he left."
Furthermore, the FC Porto supremo pointed out there's no need for defensive reinforcements, highlighting: "We already have Martin, who is a Dutch international, Herrera, who is playing at the Copa America with Mexico, plus Maicon and Alex Sandro."
Javier Diaz, who represents 24-year-old Bartra, has previously acknowledged interest from Tottenham Hotspur to Sky Sports, although he was also clear his client "is happy" at Barcelona.
There was though an important caveat from the agent, who suggested the Spain international "wants to play more games" and "will look at the options" before any final decisions are made, regarding his future at the Camp Nou.
The key factor at the moment, which is forming the basis of all the reported interest in Bartra, is a €12 million clause valuation, apparently activated by not having reached a stipulated number of appearances, during the 2014-15 season with Barcelona.
Both Bartra and his agent have publicly mentioned this figure, even though Barcelona insist that in his most recent contract renewal signed last July, the clause valuation remains €25 million.
In terms of his playing opportunities looking ahead, Mundo Deportivo believe another important aspect for the player to weigh up, will be the knowledge he must compete with Pique, Mascherano, Vermaelen and Mathieu, for a place in central defence at Barcelona.
Though it is acknowledged that Bartra's primary desire is to stay with the treble winners, there is the growing sensation that if he can't get assurances of more games in the 2015-16 season, his willingness to move elsewhere will increase significantly.
Tottenham aren't the only Premier League club monitoring the situation, given reports from TalkSport that Liverpool are keen to throw their hat into the ring, as they seek to make significant improvements to their squad.