Cech joined the Gunners in the summer of 2015 when Mourinho had just won the Premier League at Stamford Bridge.
The Daily Star has published an email from Mourinho discussing the deal.
Mourinho said the former Southampton duo were "s***" under Wenger but he would make them top players.
The 53-year-old wrote in an email: "Mister Wenger wants Cech and he thinks about money...he is wrong!!!
"What I want is to f*** him...Want Cech?
"OK, I want Walcott or Oxlade-Chamberlain!!!
"Want a top goalkeeper?
"OK, I want a young player, s*** with you but I can make him top."