A loan is understood to be the preferred structure, with Schalke potentially able to secure an option, or even an obligation, to make the move permanent further down the line.
That could prove costly: Lindström remains under contract with Napoli until 2028, having joined the Serie A club from Eintracht Frankfurt in 2023 for around €30m plus bonuses, a move that never worked out, with the Danish international failing to register a single goal or assist in 29 appearances during his debut season in Italy.
He was subsequently sent out on loan to Everton and, last season, Wolfsburg, where he was unable to prevent the club's relegation from the Bundesliga and was widely regarded as one of the division's biggest flops of the campaign.
Schalke are hoping the 26-year-old can rediscover the kind of form he showed during his time at Frankfurt, where he registered 14 goals and 14 assists in 80 appearances before his move to Naples.
The newly-promoted club have been active in recruiting players with Bundesliga pedigree this summer, having already brought in goalkeeper Kevin Müller from Heidenheim, striker Junior Adamu from Freiburg and defender Robin Gosens, a boyhood Schalke fan, from Union Berlin, and are also working on a separate loan for Besiktas defender Felix Uduokhai.
Lindström, an 18-times capped Denmark international, represents a further gamble on proven top-flight experience as Schalke look to establish themselves back in the German top division after promotion. His market value has fallen sharply since his Frankfurt days, when it stood at around €28m, to closer to €18m by the time he left for Wolfsburg last summer, reflecting how far his stock has dropped over two largely forgettable loan spells.