Cech would like to join Arsenal, but the Premier League champions are reluctant to let him move there unless they receive a home-grown player as part of the deal.
PSG are also interested and Chelsea would prefer to sell to the French champions for a fee of around £11m. Cech, who has been at Chelsea for 11 seasons and has a year left on his contract, would rather remain in London, where his family is settled.
The 33-year-old returned to London to meet Chelsea with his representatives after playing in the Czech Republic’s 2-1 defeat in their European Qualifier against Iceland
Cech spent last season as second choice to Thibaut Courtois and featured in just seven Premier League games – it was the first time he has not been No 1 at Stamford Bridge.
The four-time Premier League winner has made over 500 appearances for Chelsea since joining in the summer of 2004 from Rennes for £7m.
His performances helped Chelsea win the title in Jose Mourinho’s first season as manager – they also won the league the following season but Cech missed three months of the 2006-07 season after fracturing his skull against Reading.
Cech has no memory of the incident and he has worn a protective skull cap ever since his return from the injury.