The European Commission gave the deal the go-ahead last September on condition that Edizione Holding sold all direct and indirect stakes in Blu. The European regulator agreed on a timetable for the divestment which, it said, is still running.
However, the commission believed Pirelli and Edizione Holding have been dragging their feet on the sale.
"The sale of Blu is a condition for clearing the deal and the parties involved are under obligation to explore every possibility to comply with the undertaking given," Monti said.
"It does not appear that until now sufficient consideration has been given to the interest expressed by several potential bidders," he added.
The commission refused to name the bidders. Its main concern is that September's deal gives Pirelli control over two of the four mobile phone operators in Italy: the market leader Telecom Italia Mobile and Blu.
It declined to comment on how much time Pirelli and Edizione have left to sell Blu. It said it is warning the companies now ahead of Tuesday's shareholders meeting at Blu.