The two clubs are believed to have reached an agreement over a season-long loan deal - with an option to buy for £30m - for the Spaniard earlier on deadline day.
The Blues are supposedly set to pay €5m (£4.3m) for the temporary signing of Saul, but the Spaniard's arrival is now rumoured to have been plunged into fresh doubt.
According to Sky Sports News, paperwork problems on Atletico's side are holding up the completion of the deal, which is now 'touch-and-go' to be finalised before midnight.
The 26-year-old was previously linked with a switch to Manchester United and Liverpool after reportedly being told that he was free to leave the Wanda Metropolitano this summer, but he may remain in the Spanish capital should the necessary admin not be completed.
Saul has started two of Atletico's three La Liga games so far in the 2021-22 season, and his contract with the La Liga giants does not expire until 2026. body check tags ::