Graham Potter has made bolstering his midfield a priority in January with N'Golo Kante and Denis Zakaria out injured.
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The Blues also know they have to strengthen in the middle of the park with Kante and Jorginho in the final six months of their contract.
It remains to be seen whether the west London outfit activate Enzo Fernandez's £106million release clause at Benfica, while Brighton's Moises Caicedo will cost at least £75m.
And according to The Times, this has led Chelsea to step up their interest in Everton's £50m-rated Onana, who only joined the club from Lille last summer.
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Regarded as an alternative to Fernandez and Caicedo, Chelsea are claimed to be keen on bringing the 21-year-old to Stamford Bridge this month.
Foot Mercato have stated that Chelsea had made an offer to sign the four-cap Belgium international.
But in a twist, the player has turned down a move to link up with Graham Potter's side.
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Belgian journalist Sacha Tavolieri has said that Onana instead wants to remain at Goodison Park to help them out in their fight against relegation.
Everton currently sit in 19th spot in the Premier League table, with the Merseyside outfit without a win in the top-flight since October.
Their recent 2-0 defeat at West Ham saw Frank Lampard sacked on Monday, with the club's next two games being against table-toppers Arsenal and rivals Liverpool.
Chelsea now have a decision to make at whether to go back in for Fernandez or Caicedo, or to now move onto another alternative.
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While Everton have received a boost with Onana set to stay, they are poised to see winger Anthony Gordon depart.
Newcastle are known to be keen on landing the 21-year-old, with the youngster absent from training this week.