Gudmundsson, 27, impressed throughout his debut Premier League season at Leeds United, making 35 appearances as the club finished comfortably in mid-table.
He joined from Lille for €12m in the summer of 2025 on a contract running to 2029 and established himself as one of the better attacking left-backs among the promoted sides.
Chelsea have already agreed a deal for Atalanta's Marco Palestra — a versatile player who can cover the left flank among other positions — but are understood to want a specialist left-back in addition to that signing.
Gudmundsson fits the profile and according to Expressen sources, a move to Stamford Bridge would be considered a "dream" by the Sweden international, who is currently at the 2026 World Cup.
Leeds would not sell cheaply. Having paid €12m for Gudmundsson a year ago with his contract running four years, the club are under no financial pressure to accept an approach below market value.
Leeds manager Daniel Farke has spoken warmly of Gudmundsson's contribution throughout the season.
Chelsea's broad summer recruitment need — they must replace Cucurella and potentially Malo Gusto, while raising significant sales income after finishing tenth last season — makes Gudmundsson an attractive option given his Premier League-proven status and the relatively modest fee Leeds would require.