Larsson, 22, travelled to London for negotiations after Frankfurt granted the Sweden international permission to discuss a move, according to Sky Germany.
Crystal Palace are one of two Premier League clubs in the running, with Frankfurt holding out for a fee in the region of €25m.
Eintracht Frankfurt are ready to reinvest any proceeds in the market, with the Bundesliga club having reached a basic agreement with Lillian Brassier and Stade Rennes over a permanent transfer worth around €8.5m plus bonuses.
The Frenchman, viewed as Frankfurt's first-choice option to fill any central defensive gap, would sign a long-term contract, with his medical and travel arrangements still to be finalised.
Meanwhile, Palace's move for Club Brugge centre-back Joel Ordóñez has hit a snag after his medical revealed his recovery from a broken metatarsal to be further behind than the club initially understood. Palace are now weighing up whether to proceed with a deal that was structured as an initial loan with an option to buy at the end of the season.
BBC Sport reported this week that Palace hijacked Aston Villa's move for the Ecuador international, agreeing terms before the complication emerged. Crystal Palace were aware of the injury when negotiating, but the issue is understood to be more serious than first believed.
The Eagles have accelerated their search for defensive reinforcements since Chadi Riad was carried off on a stretcher during Saturday's game against Everton. They completed the loan signing of Axel Disasi from Chelsea on Wednesday but are keen to add a further central defender before the transfer window closes.
Palace's business this summer follows a landmark 2025-26 campaign in which they won the FA Cup and the Conference League, results that hand new manager Pierre Sage a heavier fixture list to navigate in his first season at Selhurst Park.
The Frenchman replaced Oliver Glasner over the summer after leading Lens to a runners-up finish in Ligue 1, and centre-back has been identified as a priority position given the club's threadbare options following Chadi Riad's injury and the summer departure of Maxence Lacroix to Chelsea.