Antonio Conte’s side had agreed a fee for the England international on Monday and were trying to finalise a transfer as soon as possible in the fear that the Reds may also register their interest and shift matters.
The 24-year-old did not aid the strategy of the Premier League champions, though, showing no speed in undertaking a medical or working through any of the other formalities to wrap up the switch.
Oxlade-Chamberlain would prefer to line up under Jurgen Klopp and feels he has more of a chance at featuring in his preferred midfield role at Anfield if he impresses.
The versatile player, currently with Gareth Southgate’s squad ahead of Friday’s World Cup qualifier with Malta, is waiting on Liverpool to submit a formal proposal to Arsenal.
However, earlier in the window, the Gunners had expressed they would not sanction a sale to the Reds.
If there is a softening of that position now, Liverpool - currently working on a club-record move for Monaco’s Thomas Lemar worth over £70m inclusive of extras - would pursue a deal.
Oxlade-Chamberlain, who could see out the final year of his Arsenal contract should that fail to materialise, has not been a priority target for Klopp, but is viewed as a good candidate to supplement their main business.