The Blues had their transfer ban cut in half last week, handing Frank Lampard the chance to bolster his squad mid-season.
Lampard is eager to add more attacking options to his side and Crystal Palace winger Zaha is being strongly considered by the Stamford Bridge hierarchy, according to the Guardian.
The Ivory Coast international was keen to leave Selhurst Park over the summer, but moves to Arsenal and Everton failed to materialise.
He remains determined to play at the top level of the game and is a realistic target for Chelsea, who have handed Lampard a £150 million transfer budget.
Lampard flagged up his side’s reduced creativity since the departure of Eden Hazard to Real Madrid after their 2-1 Champions League victory over Lille on Tuesday.
But Palace are likely to demand around £80m for their star man, who has a contract there until 2023.
Chelsea are set to lose Pedro and Willian at the end of the season when their contracts expire, while they have been linked with Borussia Dortmund’s Jadon Sancho, Lyon striker Moussa Dembele, RB Leipzig’s Timo Werner and CSKA Moscow’s Fyodor Chalov.
But Zaha is familiar with the Premier League and would also be eligible to feature in the Champions League knockout stages.
Chelsea’s hopes of signing the 27-year-old could be boosted by Palace’s interest in striker Olivier Giroud, who is out of contract with the London club in the summer and wants a January move to aid his chances of getting into France’s Euro 2020 squad.
In defence, a move for Bournemouth’s Ake would present far fewer difficulties due to a clause in his contract.
The Netherlands international departed Stamford Bridge for Eddie Howe’s side in 2017 with a buy-back clause set at £40m included in the deal.
Ake, who is currently out injured, has impressed for the Cherries and would otherwise command a higher fee.
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