Lindstrom was collected from the airport and taken directly to undergo the mandatory medical check, according to Bild, though the paper reports that Napoli and Schalke have not yet reached full agreement on the terms of the deal.
The two clubs remain apart on the structure: Napoli want a loan with an obligation for Schalke to buy the 26-year-old at the end of the season, while Schalke are pushing for a loan with an option to buy in the region of €5m instead.
Lindstrom enjoyed considerable success in Germany during a previous spell at Eintracht Frankfurt, form that persuaded Napoli to sign him for around €30m plus add-ons in 2023, but he has never come close to justifying that fee in Italy, failing to register a single goal or assist in 29 competitive appearances during his debut season.
Loan spells at Everton and, most recently, Wolfsburg failed to reignite his career, with Lindstrom widely regarded as one of last season's biggest Bundesliga flops after Wolfsburg's relegation. He remains under contract at Napoli until the summer of 2028.
Should the move go through, Lindstrom would become part of a significant summer rebuild at Schalke as the club prepares for a return to the Bundesliga after clinching the 2. Bundesliga title, joining fellow new arrivals Robin Gosens, Satoshi Tanaka and Junior Adamu, plus goalkeeper Kevin Muller, who has signed permanently after his own loan spell.
Schalke are hopeful that a return to Germany and a fresh start away from Naples can help Lindstrom recapture the form that once made him one of the most exciting young talents to emerge from Denmark.
A similar loan structure was previously used by Schalke to sign Robin Gosens this summer, with the club open to repeating that model given their limited spending power outside of television revenue as a newly promoted side.
Lindstrom, who has 18 caps for Denmark, will hope a move back to a country where he once excelled can arrest a career that has stalled significantly since his big-money switch to Serie A three years ago.