The Daily Mail report that talks over a new deal are in early stages and an improved offer is expected from the Blues, but the rejection has put Spanish giants Real Madrid, long thought to be interested Manchester United's David de Gea, on red alert.
Madrid have also cast an eye over the situation of AC Milan shot-stopper Gianluigi Donnarumma, who reportedly declined a recent contract offer from the Italian side, as they look for an improvement on current first-team goalie Keylor Navas.
De Gea had been Madrid's first choice but United's valuation of the Spain international has deterred them making a bid and Zinedine Zidane's side could up their interest in Courtois should the Belgium international continue to dismiss contract proposals.
Chelsea are thought to be prioritising new signings but new deals for manager Antonio Conte and star winger Eden Hazard are yet to be agreed as Chelsea head into the 2017-18 Premier League season looking to defend their title.
Meanwhile, former Chelsea defender John Terry has received a contract offer from Championship side Birmingham City, who are currently managed by former Tottenham boss Harry Redknapp.
The former England captain was released at the end of his contract with the Stamford Bridge side and Redknapp has revealed he wants to sign the 36-year-old.
Redknapp said: "