Williams told reporters at the Spanish Grand Prix that she had discussed compensation with the race promoter in Baku after the April 26 incident.
"They have been very accommodating and seem to be moving things pretty quickly forwards. So I'm pleased," she said.
"It will go through the (circuit) insurers', they understand it needs to move sooner rather than later. So we are in the process now of working out the cost of it to us and we need to file that and we'll go from there."
Williams could not give a financial estimate, which some commentators have speculated could be more than half a million dollars.
"Our priority was to get the repair work done and then we'll go through the analysis to understand exactly how much of a cost there is," she said.
British rookie Russell ran over the loose manhole cover at speed in Friday practise, smashing the floor.
"If that was 10-15mm higher, it was going straight into where I'm sat. It could have been much worse," the driver commented afterwards.
Polish team mate Robert Kubica also suffered a big accident in the first phase of qualifying.
Williams said both chassis had been repaired and brought to Spain, along with a spare.
She said the former champions, without a point and last in the standings with an uncompetitive car despite having the same engine as dominant Mercedes, had brought upgrades and test parts to the track.
"In our history we've never given up on a season," she declared. "Clearly we know where we are and that it will be incredibly difficult to make up the gap even to P9 (ninth place overall).
"We have a number of issues at the moment. There are a number, mechanical in particular, that we've understood," added the boss. "So we have a particular issue with our brake system at the moment that we believe we've found a solution to."
(Reporting by Alan Baldwin, editing by Christian Radnedge)
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