"We're very careful to say this is not 1977, this is not 77,000 at Giants Stadium, we don't have Pele and Beckenbauer," Stover replies when asked about the task he faces in trying to live up to the Cosmos' stellar past.
"We have a good squad and we play good soccer and we will grow from there. It needs to be built up, we can't start at that level overnight."
But the Cosmos have been able to recruit one player whose caliber is undeniable.
Senna enjoyed a successful career in Europe with Spanish club Villarreal, helping the team reach the 2006 Champions League semifinals.
The midfielder also represented his adopted homeland at international level and he was a key member of the Spain team which won Euro 2008 and kick started La Roja's recent period of dominance.
The Cosmos' legacy is built on the recruitment of players like Senna and Pele, but Stover has more realistic goals this time around.
"Marcos is obviously a great player and a recognizable star," he explains. "I think that's the type of player we're looking for.
"We also know that we have to have a sustainable model. We can't over spend, we can't bring in 11 superstars right now, that's not going to do anybody any good. We like our roster now and we like who we are, every team is always evolving."
Carlos Mendes is one of Senna's new teammates and a genuine New Yorker.
The defender boasts a respectable pedigree within U.S. soccer and is a veteran of six years with the Red Bulls.
Despite the weight of history on his new team's shoulders, Mendes is relishing the chance to represent a club with such an illustrious name.
"It's an honor," insists the 32-year-old.
"We can never duplicate that. You're never going to match that team, some of the best players in the world.
"Hopefully we can play attractive soccer, something the fans can be proud of and we can bring some championships back to New York. That's our main focus starting August 3."
Mendes is part of a team which has been brought together in little over two months by the Cosmos' hierarchy, with coach Savarese at the heart of the effort.
The Venezuelan was a journeyman striker in the MLS, best known for a prolific two-year spell with the New York/New Jersey Metrostars between 1996 and 1998.
He has a team at his disposal which boasts a European champion, but also contains players looking for a second chance at a football career.
"We are very satisfied with what we're building right now, with the players and the family we're creating at the New York Cosmos," says the former Venezuela international.
"I'm having fun. I think this is a great job, with a great organization with a great name. We don't have time to think about pressure, we just have to keep working and make sure we build a new future."
What the future holds for the Cosmos is uncertain. Could the club one day join the Red Bulls in the MLS?
"It's possible," answers Stover. "We don't know. There are no discussions right now. There's no animosity between the groups.
"We just do things one way and MLS does them differently. You never know how things will grow and change over time."
After 30 years in the doldrums, the New York Cosmos are happy enough just being back on the field.