The Chelsea manager has identified Sterling as a key target this summer with new owner Todd Boehly ready to back his manager in the transfer market.
Sterling has just one year left on his contract at Manchester City and has been considering his options since the end of the 2021-22 season.
The Guardian report that a bid between £50million and £60million will be enough to bring the England international to Stamford Bridge.
While there have been positive talks between Tuchel and Sterling, personal terms have not been agreed at this stage.
Sterling joined City from Liverpool in a £49m deal in 2015 and has scored 131 goals in 339 games for the Manchester club.
While Tuchel is eager to reshape Chelsea’s attack with Romelu Lukaku poised to return to Inter Milan, reinforcements at the back are desperately needed following the departures of Antonio Rudiger and Andreas Christensen.
Chelsea are keen to sign Juventus star Matthijs De Ligt with an offer of €40m (£34.4m) plus Timo Werner already rejected by the Serie A giants.
According to Sky Sport Italia, Juventus have told Chelsea to pay €70m (£60.3m) and include Werner as part of their deal for De Ligt.
MORE : Chelsea targeting Raheem Sterling AND Ousmane Dembele as Thomas Tuchel plans to transform attack
MORE : Ousmane Dembele disappointed by Chelsea offer as Raheem Sterling approach hampers deal
For more stories like this, check our sport page.
Follow Metro Sport for the latest news on
Facebook, Twitter and Instagram.
Stay connected with us on social media platform for instant update click here to join our Twitter, & Facebook
We are now on Telegram. Click here to join our channel (@TechiUpdate) and stay updated with the latest Technology headlines.
For all the latest Football News Click Here