Goal understands the Rojiblancos have proposed both Nikola Kalinic and Gelson Martins to Chelsea in the knowledge that Morata will only be let go if a replacement can be found.
Atletico would only let one of the two go to west London as part of the Morata deal, though they are hopeful of offloading both during the January transfer window.
Kalinic arrived at the Wanda Metropolitano from AC Milan in August in a deal worth €15 million (£13.3m/$17.1m) but has struggled to adapt to Diego Simeone's style in the Spanish capital.
The Croatia international has scored just three goals in 17 appearances in all competitions and is now set to be moved on again.
Gelson, meanwhile, signed a six-year deal with Atletico having cancelled his contract with Sporting amid the controversy surrounding former club president Bruno de Carvalho.
It is likely, though, that Atletico will have to pay a fee as compensation, with reports claiming Sporting are demanding up to €105m (£93m/$120m) for the Portugal international who has contributed just a single goal and no assists in 12 appearances for Simeone's side.
The offer of a player as part of the deal has raised hope that Atletico will be able to sign Morata, with the club currently sitting second in the Liga table willing to pay a €3m loan fee to secure him until the end of the season along with an option to make the deal permanent in June.
However, they are only willing to pay half of Morata's £120,000-per-week salary while the Blues are insistent that Atleti cover the full cost.
Morata spent the weekend in Madrid holding talks with a variety of potential suitors, though Sevilla have since pulled out of the race due to the cost of signing the Spain international.
Maurizio Sarri's top target to replace Morata in his squad is Gonzalo Higuain, with the Argentine keen to end his loan spell at AC Milan and reunite with the manager who coached him during his successful period at Napoli.
And speculation regarding his future gathered pace on Wednesday after he was missing from Milan's team photo in Saudi Arabia ahead of their meeting with Juventus in the Supercoppa Italiania in Jeddah.
It is understood that the Chelsea hierarchy were cooling on the prospect of signing Higuain due to the complexity of the deal given the striker's parent club Juventus would also be involved, but the player's apparent willingness to swap Milan for London could tempt them to secure his signature.