Mahrez has been given permission by Leicester to negotiate a move away from the King Power Stadium on deadline day.
Arsenal, Manchester United and Barcelona have all been tipped to sign the Algeria international in the wake of this development.
But The Sun say he is on his way to Chelsea instead and will become the Blues' fifth summer signing after previous deals for the likes of Antonio Rudiger, Willy Caballero, Alvaro Morata and Tiemoue Bakayoko.
Manager Antonio Conte has supposedly convinced Leicester to let him go with a huge offer of £45million.
Riyad Mahrez looks set to join Chelsea from Leicester
Mahrez was pictured with a fan in Paris after leaving Algeria's training camp yesterday.
And The Sun say he was on his way to London to seal a move to Conte's Premier League champions.
Mahrez came close to joining Roma earlier in the summer.
But the Serie A giants saw three bids rejected and were ultimately unable to secure his signature.
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Riyad Mahrez: Chelsea look set to sign the Leicester star
Arsenal were thought of as serious contenders up until recently with the future of Alexis Sanchez up in the air.
Sanchez remains on Manchester City's radar today though Pep Guardiola's side are yet to launch another bid after having a £50m offer knocked back.
However, Chelsea look set to sign Mahrez instead.
Once a deal is completed he will compete with the likes of Eden Hazard, Willian and Pedro for a place in Conte's starting line-up.
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