The Dutchman, who was fired by the LaLiga outfit last October after 14 months in charge at Camp Nou, struggled at times on the Barcelona bench and was replaced by Xavi.
Koeman, who will embark on a second spell as Netherlands head coach after the World Cup in Qatar, has confirmed he attempted to bring in compatriot Wijnaldum during the final transfer window of his Barcelona tenure.
However, Koeman contends that president Laporta, then recently returned to the position as Josep Maria Bartomeu's successor, stymied any move by dragging his heels.
"I tried to sign Wijnaldum for Barca, but I failed because the president wanted to play with me more than bring in a player," Koeman said.
"That delayed the operation, and for that reason, he opted for PSG. Otherwise, he would have played for Barcelona."
Wijnaldum left Liverpool in June 2021 to join Paris Saint-Germain, but he struggled across a dismal first season, resulting in him being loaned out to Roma for the current campaign.
A serious leg injury has since left Wijnaldum sidelined, however, making it highly unlikely he will be included in the Netherlands' squad for the Qatar 2022 World Cup.