Sky sources report Cech, 33, has agreed personal terms in principle on a switch to the Emirates Stadium but we understand the two clubs are still not close to agreeing a fee and negotiations will continue this week.
The transfer fee is unknown but it will be a cash only deal, with Chelsea’s request to receive a home-grown player as part of the proposed transfer no longer being considered.
Cech is said to be grateful to Chelsea owner Roman Abramovich for allowing him to move to whatever club he chooses, even though that is now likely to be London rivals Arsenal.
The Czech Republic goalkeeper has one year left on his contract at Stamford Bridge but is searching for a new employer after spending much of last season as second choice behind Thibaut Courtois.
Cech is believed to be keen to move to the Gunners although it is believed that Blues boss Jose Mourinho would prefer him to join French champions Paris Saint-Germain.