The Liga side’s club secretary Robert Fernandez revealed the request ahead of the UEFA Super Cup final, where the 28-year-old started on the bench.
“Pedro has told me that he wants to leave,” Fernandez said on Spanish television. “Right now there is nothing [no offers].”
United have not made a formal bid but manager Louis van Gaal would like to bring Pedro to Old Trafford following Angel di Maria’s switch to Paris Saint-Germain.
That may mean meeting the £22 million buy-out clause in Pedro’s contract.
Fernandez added: “Pedro’s clause is not negotiable, but this could be his last game.”
The forward has struggled to make the Barcelona starting XI recently with Luis Suarez, Lionel Messi and Neymar all being preferred.