Goal understands Atletico have reached an agreement that would see them pay €3 million (£2.6m/$3.4m) to bring in Morata for the remainder of the campaign, with the option to pay a further €40m (£35.2m/$45.6m) to buy the Spain international at the end of the season.
Atletico are still in negotiations with Chelsea regarding the percentage of Morata's wages they will pay, with the Liga outfit hopeful of only forking out for 50% of his £120,000 per week salary before entering talks regarding a reduced contract with the player should he make the move permanent.
Atleti, however, are not currently in a position to sign off on the deal with Chelsea as they try to offload two summer signings of their own in a bid to clear space on their wage bill .
Forward Nikola Kalinic arrived from AC Milan in the summer but has struggled to adapt to Diego Simeone's style of play, scoring just four goals in 18 matches.
The Rojiblancos are also trying to sell winger Gelson Martins, who signed a six-year deal after joining on a free transfer from Sporting having cancelled his contract with the Portuguese giants.
The hold-up in offloading Morata is having an effect on Chelsea’s signing of Gonzalo Higuain from AC Milan, which is effectively complete.
Chelsea are keen to get Morata off their wage bill before bringing in Higuain, while Milan themselves must find a replacement for the Argentina international, with Genoa’s Krzysztof Piatek their primary target and likely to cost around €40m (£35.2m/$45.6m).
Higuain has an arrangement to join Chelsea on a six-month loan which can either be extended for a further year or turned into a permanent move in the summer, though that would lead to fresh contract negotiations for the 31-year-old.
The former Real Madrid forward will reunite with Blues boss Maurizio Sarri, who worked with Higuain at Napoli and played a key role in the striker matching the record for the most goals in a single Serie A season with 36 in 2015-16.
Higuain and Morata are not the only strikers with Chelsea links on the move in January, with Michy Batshuayi's departure from Stamford Bridge adding further complications to a busy month in west London.
With his loan spell at Valencia having been cut short, Chelsea are hopeful of being able to sell the 25-year-old for around €45m (£40m/$51.3m).
This has stalled Batshuayi's agreed loan move to Monaco , and with the Ligue 1 strugglers now looking into the possibility of signing Kalinic, the Belgium international's reunion with Thierry Henry could now be off.
Everton have also shown an interest in the ex-Borussia Dortmund and Marseille forward but their valuation falls well short of what Chelsea are looking for.
He could yet be used as part of the deal to sign Higuain if Milan struggle to find a viable replacement elsewhere while Crystal Palace are also reportedly keen.
Meanwhile, Chelsea are also in talks with Zenit’s Leandro Paredes over a move for around €30m (£27m/$34m), though the Russian club value him at €40m (£36m/$46m).
There is hope that Chelsea can complete all their January business ahead of the second leg of their Carabao Cup semi-final against Tottenham next Thursday, but their match with Arsenal in the Premier League on Saturday is set to come too soon for the likes of Higuain.
Additional reporting from Ruben Uria and Romeo Agresti.