Memphis, 28, is out of contract in the summer and has made just four appearances in all competitions this season, with Robert Lewandowski, Ousmane Dembele, Raphinha, Ansu Fati and Ferran Torres all preferred by Barca coach Xavi Hernandez.
Sources have told ESPN that Atletico have received a positive response from Memphis' camp but negotiations with Barca are not as straightforward.
The Catalan club would prefer to transfer him on a permanent basis for a small fee, although they would also consider a loan depending on the terms of the agreement.
Barca would also like to be able to replace Memphis, if possible, but their hands are tied due to LaLiga's financial fair play rules and any incomings would be dependent on how much salary space the Dutch forward's departure creates.
Following a lack of minutes under Xavi, sources have confirmed that several clubs have asked about Memphis' availability, with the former Manchester United player expected to leave for nothing in the summer if he does not move on in January.
In total, Memphis has made 42 appearances for Barca and scored 14 goals.