Williams appears to have been nominated as the supplier of a Pirelli test car for 2021.
Earlier, we reported that F1's official supplier was seeking a test car to conduct development of the 18 inch tyres for 2021 later this year.
"One of the biggest problems at the moment is to find a suitable test car," said Pirelli's Mario Isola.
Tobias Gruner, a journalist for Germany's Auto Motor und Sport, reports that the teams are happy with Williams.
"Engineers worried about unfair advantage," he tweeted. "But with Williams apparently being far behind it would be ok.
"We don't know whether Williams is interested or has the means to supply a mule car. If they decline Pirelli has to look for a different solution," Gruner added.
Ahead of the 2019 season opener in Australia, Williams is in full crisis, with technical director Paddy Lowe put on "leave".
Auto Motor und Sport reports that Lowe will almost certainly leave the team completely.
"He is also a shareholder and board member," said Gruner.
He said it is rumoured that it was "too expensive" for Williams to simply sack Lowe.
"If you believe the rumours, the cost of the separation is less if the decision is delayed a few weeks. It is therefore hard to imagine that Lowe will come back to his job after the break."
Another rumour is that Rob Smedley, who recently left Williams and took up a role with Liberty Media, could return to the team to replace Lowe.
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