The SNP is giving "serious consideration" to a request to reinstate Edinburgh West MP Michelle Thomson, party sources at Westminster have told BBC Scotland.
Ms Thomson withdrew from the SNP whip last year amid an ongoing police investigation into property deals.
She has been sitting as an independent MP in the House of Commons since then.
But a meeting of SNP MPs on Tuesday evening asked the party's national executive to consider the matter.
It is understood that the motion received unanimous backing from those present.
Ms Thomson denies acting unlawfully after being linked with property deals involving a solicitor who has since been struck off.
The transactions were said to have been carried out before Ms Thomson was elected as an MP in May 2015.
Speaking shortly after the allegations were first published by the Sunday Times newspaper, Scottish First Minister Nicola Sturgeon said they would represent "behaviour that I find completely unacceptable" if they were proven to be true.
Ms Thomson has been linked with property deals involving Christopher Hales, a solicitor who was struck off for professional misconduct by the Scottish Solicitors' Disciplinary Tribunal (SSDT) in May 2014 in connection with 13 transactions in 2010 and 2011.
The SSDT said Mr Hales failed to provide mortgage companies with key information used to prevent fraud and must have been aware that there was a possibility he was facilitating mortgage fraud, whether or not it occurred.
Prosecutors subsequently instructed police to carry out an investigation into alleged irregularities relating to property deals in the year 2010/11 after the case was referred to the Crown Office by the Law Society of Scotland.
Responding to the calls for Ms Thomson to be reinstated by the SNP, Scottish Labour MSP Neil Findlay said: "There are still many questions to be answered about this case. But given what we do know, it would be wrong for Michelle Thomson to return as an SNP MP."