The seven - referred to as B, N, O, Q, R, U and V - want to challenge the way in which Police Service of Northern Ireland detectives are conducting their historical inquiry.
Mr Justice Ouseley will have to decide whether or not the soldiers have "an arguable case" to go to a full hearing.
Their written arguments were submitted by law firm Devonshires Solicitors, identifying them through letters of the alphabet given to the soldiers during the Saville inquiry into the deaths of 14 civil rights protesters in Londonderry.
The legal action follows a decision by Bloody Sunday investigators to arrest a 66-year-old former lance corporal.
He was released by the PSNI on Wednesday evening after he was interviewed in Belfast for several days.
Thirteen people were killed by members of the Parachute Regiment on the day of the incident in Derry's Bogside. Another victim of the shootings died in hospital four months later.
Police in Northern Ireland launched a murder investigation in 2012 - a probe initiated after a Government-commissioned inquiry, undertaken by Lord Saville, found that none of the victims was posing a threat to soldiers when they were shot.
Following the publication of the Saville report in 2010, Prime Minister David Cameron apologised for the Army's actions, branding them "unjustified and unjustifiable".
In September, the PSNI told bereaved families they intended to interview a number of former soldiers about their involvement on the day.
On Tuesday, detectives made their first arrest in the case when they detained a 66-year-old former paratrooper in Co Antrim.
The pensioner was released on bail on Wednesday night pending further police enquiries.
It is understood the pensioner was arrested on suspicion of the murders of William Nash, 19, John Young, 17, and Michael McDaid, 20, all of whom were shot dead in close proximity to one another at a rubble barricade on Rossville Street.
It is believed the former soldier was also questioned about the attempted murder of William Nash's father Alexander. Mr Nash came to the barrier to save his son but was shot in the arm and body.
It is understood the soldier gave evidence to the Saville Inquiry under the cipher Lance Corporal J.