This is according to the Express, who understand that Jese - the highly-rated 21-year-old forward - has become Mourinho's latest transfer target.
The Blues will offer £15 million for the Spain Under-21 international, who returned to action last month following a serious knee injury sustained in March, and a further £20 million for the world-class France international Varane.
Mourinho handed Varane his La Liga debut
Varane, widely considered the best young centre-back on the planet, is also wanted by Manchester United and Arsenal.
However, the 21-year-old might be more inclined to join his former manager Mourinho at Stamford Bridge. The central defender was handed his La Liga debut by the revered Portuguese coach in 2011 and went on to cement his status as one of the best defenders in the Spanish top flight within the space of 18 months.
Varane contracted to Real Madrid until 2020
Real Madrid reportedly value Varane at around the £20 million-mark - which seems awfully low for arguably the best young defender in world football whose contract doesn't expire until 2020.
The Frenchman put pen-to-paper on a new six-year deal in September - and Real Madrid boss Carlo Ancelotti will surely do everything in his power to keep the youngster at the Bernabeu.
Mourinho regards Varane as a natural successor to John Terry, the Blues' long-serving captain whose contract expires at the end of this season.
Jese: La Liga's breakthrough star
Jese, meanwhile, was one of La Liga's breakthrough stars last season. The 5ft 10in live-wire forward finished his first full campaign as a Real Madrid senior player with eight goals from 31 appearances - plus winners' medals for the Copa del Rey and Champions League.
He added a FIFA Club World Cup medal to his collection last month, but was an unused substitute in the final against San Lorenzo.
The intense competition for places at the Bernabeu means Jese could be tempted to move to Chelsea - but only if Mourinho can offer him more playing time.
Competition is also fierce at Stamford Bridge - but the Spaniard has the potential to become a first-choice striker for just about every club in the world.