The Italian supplier is poised to reveal the fruits of its investigation into Sebastian Vettel's failure at Spa-Francorchamps.
And Pirelli could also force teams to follow strict new guidelines on maximum engine set life, as well as camber settings and mandatory tire pressures.
But an unnamed team boss told Speed Week on Thursday: "We have received no new directives.
"But I do think that Pirelli will issue a recommendation on how many laps should be done with the compounds.
"Then, when a team uses it for longer than that, they can say 'What do you want from us? You didn't keep to the guidelines!'"
There is widespread skepticism, however, about Pirelli's standing theory that excessive wear due to Ferrari's ambitious strategy in Belgium caused the Vettel blowup.
"Why, then," said the unnamed team boss, "was Sebastian able to maintain such consistency in his fight against Grosjean?"