The 20-year-old fell in a stairwell at Celtic Park during Scotland’s qualifier for the 2016 European Championships against Ireland in November 2014.
Mr McSeveney, from Cumnock in Ayrshire, died from his injuries after being taken to Glasgow Royal Infirmary from Exit 33 of the stadium.
Speaking on behalf of the family, lawyers Thompsons Solicitors stated that they believed the club to have “failed in its duty of care to protect” Mr McSeveney.
“It is our firm belief that the football club failed in its duty of care to protect this young man leading to this awful accident,” partner Patrick McGuire said.
“The fact that they have now taken the obvious measure to make the area in question safer by erecting safety nets proves this.
“We will be fighting hard to make sure they family receive the justice they deserve.”
However, the club do not “accept liability for the accident” and believe Celtic Park to be a “very safe environment”.
A spokesman for Celtic said: “Celtic Football Club has considerable sympathy with the McSeveney family for their terrible loss following this tragic accident.
“However, and while the club’s sympathy is in no sense diminished, the club does not accept liability for the accident.
“Celtic Park is a very safe environment and complies with all applicable building standards.
“Celtic Park is regularly inspected and certified as safe by the relevant authorities, including an investigation immediately following the accident.
“The matter is in the hands of the club’s insurers and solicitors and it would not be appropriate to comment further at this time.”