Palace are seeking a new centre-half signing after the sale of Marc Guehi to Manchester City this week.
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Sky Sports says Acheampong has emerged as a top name for Palace in the final week of the January market.
The young Blues defender is one of several players being discussed internally at Palace.
No formal talks between the clubs have yet to begin. However, the relationship between Chelsea and Crystal Palace is described as good, after several players have moved between the clubs in recent years.
Last season, both Trevoh Chalobah and Ben Chilwell were loaned from Chelsea to Palace.
Before that, Marc Guehi and Conor Gallagher, among others, have taken the same path.