The paper claim Arsenal have rejected Chelsea's advances, and told them they do not intend to raise heir cash offer of £10 million for Cech.
Mourinho originally said he would not stand in Cech's way of his next destination, but appears to be digging his heels in to try and make a move to the Gunners untenable.
Arsenal emerged as a real threat to Chelsea's title charge over the past few months of the season, let down by their own poor start to the season.
Signing Cech, 33, would give the Gunners a serious boost, with the goalkeeper seen as more dependable than Arsenal number one David Ospina, despite losing his Chelsea place to Thibaut Courtois.
Arsenal would be loathe to let a talent like Oxlade-Chamberlain go despite the lure of signing Cech. The England international midfielder had a difficult injury interrupted season but remains a big talent and has potential to be a key player for the Gunners for the next decade.
There is a reason Chelsea want to sign him, and he is not the sort of player Arsenal should be trading away for a potential short-term win in Cech.
If anybody was in doubt just how highly Arsenal fans regard Oxlade-Chamberlain, the reaction via Twitter to the reports tells it's own story...
No one's getting the OX Theo or any of our First Teamers Do one Maureen Mirror and whoever else Keep your Cech clown #AFC— Shaheen Ashraf (@topgooner100) June 16, 2015
Can't believe Mourinho asking for the Ox or Walcott before he sells #afc Cech— Omena (@Suave64) June 16, 2015
lol Jose can keep Cech, not letting Ox go— Philip (@zwz121) June 16, 2015
Jose Mourinho wants the ox or theo to be included in any deal for Cech..... Jose must think he's dealing with west brom— Jason Alexander™ (@MrJasonAlex) June 16, 2015
Mourinho is completely delusional if he thinks he has 1% chance to get The Ox— The Wilsh (@The_Wilsh) June 16, 2015
Hahaha Mourinho wants the Ox. What is he smoking over there at the Bridge?— Jad (@jad_daou) June 16, 2015
If Mourinho really want the Ox, it's simple... £30m plus Cech.— GTID (@MesutAFC) June 16, 2015