The 18-year-old Italy international began his career with Inter Milan before leaving in 2020 to join Austrian top-flight champions Zurich, where he scored 10 goals in 36 appearances last season.
Reports in the media have suggested that Leeds are in talks with Zurich over a possible deal for Gnonto, who is allegedly valued at around £5m.
Speaking at a press conference ahead of Leeds' Premier League clash with Chelsea, Marsch confirmed the club's interest in Gnonto, who has less than 12 months remaining on his contract.
"We know him. We think very highly of him. Young and talented," said the American. "We are very active in pursuing things and we have some strategies and let's see how they play out.
"We still have time and there will be movement (in the transfer market). Dominoes will fall and we have to act on those situations. A long time since our last transfer, but the work behind the scenes has been very active."
Marsch has stated, however, that the teenage forward would not be integrated into his first-team plans immediately should he arrive at Elland Road this summer.
"[Gnonto is] not Premier League ready, but he would be a long-term project, Marsch added. "This window or in the future, unclear. (Director of football) Victor [Orta] is incredibly organised in looking at now, in the winter, next summer, two years from now. How everything pieces together.
"All the teams in the Premier League, which players are locked in for the longest, we are among the players with the longest contracts."
Marsch has made eight signings so far this summer, with Brenden Aaronson, Rasmus Kristensen, Tyler Adams, Marc Roca, Luis Sinisterra, Joel Robles, Darko Gyabi and Sonny Perkins all arriving at Elland Road for a combined fee of just over £80m.
The American boss has refused to rule out the prospect of signing a new striker before the September 1 deadline amid concerns over the fitness of Patrick Bamford.
The 28-year-old endured a frustrating 2021-22 campaign with injuries and is doubtful for Sunday's game against Chelsea after sustaining a minor groin problem in the 2-2 draw at Southampton last weekend.
"I still feel to balance out our squad effectively it would be helpful (to sign a striker), but we need the right guy," Marsch added.
"I don't want someone that takes three months to adapt and educate and not be ready to help us. Variables on their preparedness, understand our football, the league, play with this quality at this level. Ready to play. Execute our match plans."
After avoiding relegation to the Championship on the final day of last season, Leeds have made a promising start to the new campaign, accumulating four points from their opening two Premier League matches against Wolverhampton Wanderers and Southampton.
The Whites are now preparing for a challenging encounter against Chelsea, who secured a comfortable 3-0 win at Elland Road last season.