Antonio Christie and Levi Walker were part of a group convicted in 2008 over the murder of Kevin Nunes.
All five were cleared following an appeal in 2012.
Staffordshire Police confirmed a claim has been made against the force but said it could not comment any further on the case.
More on this and other stories from Stoke and Staffordshire
A police investigation was launched after the body of 20-year-old Mr Nunes was found in a country lane in Pattingham, Staffordshire in 2002.
The Court of Appeal overturned the original convictions in 2012 after Lord Justice Hooper said a "very bad case of non-disclosure" over the credibility of a witness led to "what appears to us to be a serious perversion of the course of justice".
The Independent Police Complaints Commission (IPCC) then launched an investigation into the conduct of current Staffordshire Chief Constable Jane Sawyers, Gloucestershire Chief Constable Suzette Davenport, West Midlands Assistant Chief Constable Marcus Beale and Adrian Lee, who retired as chief constable of Northamptonshire Police in 2015.
All four served with Staffordshire Police at the time of the investigation.
In March it was confirmed they would not face misconduct hearings over claims they failed to declare evidence in relation to the shooting, with the watchdog saying it found "no evidence of a cover-up or of wilful omission".
The IPCC said two detective constables were found to have a case to answer for misconduct, with one given management advice and the other retiring on health grounds.
Two men who were cleared of being involved in what was believed to be a gangland shooting have launched legal action against a police force.