Bowen pledged his future to West Ham United this summer despite the club's relegation to the Championship, but Palace's interest could test that commitment given the scale of the proposed offer. No formal bid has yet been submitted, according to The Sun, meaning the approach remains at the preparation stage rather than an active negotiation between the two clubs.
Palace's move is tied to the expected departure of winger Ismaila Sarr, who is closing in on a switch to Galatasaray worth around £34 million.
Sarr has made clear his ambition to play Champions League football, and Turkey's reigning champions are hopeful of concluding the deal within days, having already had an opening bid rejected by Palace.
New Eagles boss Pierre Sage left Sarr out of the squad for Saturday's 2-0 defeat at Everton, though the manager has since said publicly that he wants Sarr to stay and denied the club is actively trying to sell him, citing the player's three years remaining on contract and a groin issue as the reason for his absence.
Bowen, 29, managed just 11 goals in all competitions last season as West Ham were relegated on the final day, a downturn that also contributed to his omission from England's World Cup squad this summer.
A move to Crystal Palace would offer a route back into contention for Thomas Tuchel's side, given the club's continued participation in European competition following last season's Conference League triumph.
For West Ham, a sale of their captain would ease some of the financial pressure created by relegation, even if it risks a significant backlash among supporters given Bowen's recent public commitment to the club.
Sarr, for his part, has been prolific during his time at Palace, scoring 21 goals last season and playing a leading role in the club's run to Conference League glory.