Stephen Gethins is expected to rule himself out of the race to be the SNP’s deputy leader.
The North East Fife MP is a senior figure in the party’s Westminster group as its international affairs and Europe spokesman.
However, The Courier understands he will not launch a bid to be Nicola Sturgeon’s under-study.
Pete Wishart, who represents Perth and North Perthshire and is the longest-serving MP in the SNP’s current crop, is weighing up whether to go for the job.
Other Tayside and Fife MPs who have not ruled themselves out are Dundee West’s
Chris Law, who could be a grassroots favourite following his high-profile independence campaigning in 2014, and Peter Grant, the former leader of Fife Council who took Glenrothes in the SNP’s 2015 surge.
Stewart Hosie, the Dundee East MP, who resigned as the SNP’s deputy leader in 2016, is not putting himself forward.
It is thought an MP is most likely to take up the deputy position, which has been left vacant by the resignation this month of Angus Robertson, who lost his Moray seat in the Commons last year.
In his resignation letter, Mr Robertson said he could no longer act as Ms Sturgeon’s eyes and ears in Westminster.
Others being touted for the job include Kirsty Blackman, the Aberdeen North MP; Tommy Sheppard, an Edinburgh MP, and James Dornan, a Glasgow MSP.