However, the administrator has hinted that he wouldn’t stand in the way of a move.
Gignac completed something of a surprise move to Mexican football when he left Olympique de Marseille last summer and wasted little time in making an impact in Central America.
He ended the season as the top scorer in the Liga MX after bagging 15 goals in the Torneo Apertura.
His form earned him a spot in France’s Euro 2016 squad, and he was almost the hero in the final against Portugal when a late strike hit the post with the scores tied at 0-0.
However, any longer-term return to Europe may have to wait, with Garza confirming that no offer has been made by Barca.
“As a club, we have received nothing official from Barcelona,” Garza said on TDN programme Super Estadio.
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“If Andre has a desire to play in Barcelona, I don’t think we could prevent the opportunity if it were to present itself.”
Should Gignac bag a move, however, it remains to be seen where he would fit in at the Camp Nou considering Luis Enrique can already call upon the likes of Lionel Messi, Luis Suarez and Neymar to fill in in attacking areas.