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The newspaper claims that the Merseyside have made contact about taking the 23-year-old to Goodison Park on a temporary basis as he returns to full fitness after 11 months out with injury.
The report adds that Schalke are interested on a January swoop for Rahman, with the Bundesliga giants pleased with his services on loan last season.
Other European sides in the form of Monaco, Fenerbahce and Fiorentina have also been reported as potential suitors for the Ghanaian international.
Everton were said to the front-runners for his signature in the summer transfer window before his long-term injury prevented a deal, but they are set to reignite their bid to sign him.
Everton could do with some new signings in January and Rahman would fit the bill for Everton.
Leighton Baines is beginning to go on the decline as he ages, while understudy Cuco Martina does not fit the bill well for Everton.
Rahman is a left-sided flyer that usually operates as a full-back and is blessed with phenomenal pace.
The Blues left-back can also be used further forward on the wing and impressed during his loan spell at Schalke last season before his injury setback.
The defender has registered 23 appearances for Chelsea since his arrival in 2015 and would be able to make an immediate impact joining Everton.
Rahman has been training with Antonio Conte’s Chelsea team as he recovers from his injury and it is quite likely he will leave the Stamford Bridge on loan in the New Year.
Everton have been listed as an interested club and could have an advantage over rivals given their opportunity to offer the left-back an opportunity to play regular first-team Premier League football.
However, Rahman was performing well at German side Schalke before his knee injury and they have once again been reported as an interested side.