Morata could leave Chelsea by the end of the January transfer window with the Blues keen to offload him if they can find a replacement.
The Spain international has struggled for goals, form and confidence since making a bright start to his career at the club in 2017.
This season, Morata has scored just nine goals in 24 appearances and manager Maurizio Sarri has opted to start Eden Hazard as his main striker in recent matches.
Express Sport understands Chelsea have eyes on Callum Wilson, Gonzalo Higuain, Jamie Vardy and Maurico Icardi but have made little progress towards deals for any of them this month.
But interest in Morata from Atletico could spark a series of moves.
Atletico have Antoine Griezmann and Diego Costa in attack but it appears manager Diego Simeone wants more.
However, any hopes of Morata joining Atletico rest on Chelsea and the player reducing their demands, according to Balague.
“At Madrid might find a way to finance the cost of Morata if both player and Chelsea reduce their expectations,” Balague wrote on Twitter.
“Loan deal, including wages and payment to London club, cost €9m [£8m], Atletico would pay less.
“Chelsea would like a replacement and even an obligation to buy in the summer.
“Simeone has clearly shown his interest in the player and Atletico are trying to please him.”
But Atletico may face competition from Barcelona for Morata’s signature after Ernesto Valverde has praised the striker.
Barca are keen to sign a new forward after selling Munir El Haddadi.
Valverde said: “I can only say the same thing.
“That he’s a great player, that he’s at another team and that we respect that a lot.
“We have to look at it, it’s clear that after Munir’s departure we have a space.
“We’ll see if we can sign a player, although we have to take into account the club’s economic conditions. We will see if we can, if someone comes.”