The position became vacant after Angus Robertson lost his seat in the general election.
Ian Blackford, Joanna Cherry, Tommy Sheppard and Drew Hendry have all confirmed their candidacy. They were all first elected in 2015.
The party said its new Westminster group leader would be announced on Wednesday evening.
The SNP won the general election in Scotland, despite losing 21 seats. They will start the new parliament with 35 MPs.
Mr Robertson lost his Moray constituency seat to the Conservatives' Douglas Ross after Thursday's vote.

The General Penitentiary of Venezuela in central Guarico state was closed in October after violent clashes between inmates.
The bodies, which are in an advanced state of decomposition, were found during works to refurbish the jail.
So far none of the remains have been identified.
The grave was discovered on Thursday and the number of bodies found since has risen from seven to 14.
Forensic experts are continuing with their search and have not ruled out finding more bodies buried on the prison grounds.
On Friday, prison minister Iris Varela wrote on Twitter that she had contacted the relatives of two inmates to ask for their help identifying the remains.
The two prisoners disappeared when inmates were relocated from the General Penitentiary of Venezuela to other jails in October.
An estimated 9,000 prisoners were locked up in the jail near the town of San Juan de los Morros prior to its closure, according to non-governmental organisation A Window on Freedom.
The NGO says Venezuelan jails are woefully overcrowded and that last year 173 inmates died while in custody.
But Ms Varela told Venezuelan state broadcaster VTV that the country had taken huge steps to improve the conditions of its prisons.
She said that all of the country's women's and youth prisons had been brought up to new standards set by the Venezuelan government.
"This is an achievement without precedent of the Bolivarian Revolution and the government of our president, Nicolas Maduro," she said.
She said that President Maduro had asked her in 2014 to "impose maximum discipline" in Venezuelan jails.
"Well, here I am fulfilling the president's orders," she said.
She did not refer further to the remains found except to say that forensic tests were being carried out.
Four SNP MPs have said they are hoping to be the party's next leader at Westminster.
[NEXT_CONCEPT]
The number of bodies found in a mass grave in Venezuela's largest prison has risen to 14, the public prosecutor's office said in a statement.