The criminal allegations have been made in writing by lawyers acting for Mr Salmond, the Sunday Mail has reported.
The allegations reportedly raise concerns that evidence given in court contradicted statements later given to MSPs on a Holyrood inquiry run early last year.
An independent QC has been appointed by the Crown Office and Procurator Fiscal Service (COPFS) to investigate the allegations, along with a senior prosecutor.
Mr Salmond, the former SNP leader, who now heads up the rival pro-independence Alba Party, was cleared of 13 charges of sexual assault in a High Court trial in Edinburgh in March 2020.
He separately won a judicial review case in 2019 over the Scottish Government’s investigation and official report into harassment complaints against him, costing the taxpayer more than £500,000.
A COPFS spokesman said of the perjury allegations: “Correspondence from Mr Salmond’s solicitor has been received and will be responded to in due course.
“As is standard practice in any case regarding politicians, this will be dealt with by a procurator fiscal and independent Crown Counsel without the involvement of the law officers.”
Mr Salmond told the Sunday Mail: “I welcome the inquiries and will do everything I can to assist.
“The criminal investigations must be allowed to take their course before any other action is taken.”
Mr Salmond previously said last year he would launch fresh legal action “as a direct result of the conduct” of former permanent secretary Leslie Evans around her role in the handling of harassment complaints against him.
Following the conclusion of the criminal trial, the Scottish Government’s handling of the complaints against Mr Salmond was investigated by a committee of MSPs.
The committee concluded the First Minister misled the Scottish Parliament about a meeting she held with Mr Salmond in her home on April 2, 2018.
However, an independent investigation by James Hamilton QC ruled Ms Sturgeon did not breach the ministerial code around meetings with her predecessor, with the First Minister describing the findings as “unequivocal”.