PSG's pursuit of Messi, who is out of contract in June, has spilled into the media in recent months. Sporting director Leonardo, Neymar and Angel Di Maria have all spoken about the French club's desire to sign the Barca captain.
Speaking last week, Di Maria said there was a "big chance" of Messi moving to Paris, prompting Koeman to brand PSG "disrespectful" and accuse them of stirring the pot ahead of the first leg of their round-of-16 tie at Camp Nou on Feb. 16.
"I don't know why [PSG] do it," Koeman said in a news conference on Tuesday when asked about another week of speculation surrounding Messi's future. "If they want to speak about Leo, let them do it."
Lyon manager Rudi Garcia even became embroiled in the transfer saga this week, accusing Koeman of hypocrisy for condemning PSG's actions at the same time as publicly courting Lyon forward Memphis Depay.
"And now the Lyon coach gets involved," Koeman added. "It seems he likes to have prominence in the press. For me, it's not important.
"Look, what we have to do is prepare for the Copa del Rey semifinal against Sevilla [on Wednesday], then for Alaves on Saturday and then for PSG in the Champions League next Tuesday."
Messi, 33, will be free to leave Camp Nou after 20 years this summer if he doesn't renew his contract with the club. Sources have told ESPN he will wait until the end of the season to decide his future, giving him time to see how Koeman's side progress on the pitch and what the new president, who will be elected on March 7, can offer him.
If he does leave, PSG will face stern competition from Manchester City for his signature. Sources told ESPN this week that the Premier League leaders are still tracking Messi's situation even if they are not making as much noise as their French counterparts.
Messi is part of the Barca squad for this week's Copa del Rey semifinal first leg at Sevilla, although Barca have a mounting injury list with the PSG game on the horizon.
Barca are missing eight players for the game, with Sergino Dest (thigh), Miralem Pjanic (foot) and Martin Braithwaite (hamstring) joining Gerard Pique, Sergi Roberto, Ansu Fati, Ronald Araujo and Philippe Coutinho on the sidelines.
"I prefer to use players that are 100% fit," Koeman said of his decision to call up B team trio Konrad de la Fuente, Alex Collado and Ilaix Moriba.
"It's not the time to take risks. We have eight players out but all problems have a solution."