Nexstar Media Group Inc is among the suitors, according to the report.
The report said an agreement could be reached soon, though the talks could still fall apart. There are other interested parties as well, but the discussions with Nexstar are most advanced, it added.
The details of the other parties involved and the exact time by when the deal could be reached was not known immediately, according to the report.
AT&T, ViacomCBS, CW Network, and Nexstar Media did not immediately respond to Reuters' request for comment.
The most prevalent scenario is Nexstar taking a controlling stake in CW, with CBS and WarnerMedia remaining as minority owners and receiving commitments to be the primary program suppliers for the network, the report said.
CBS and WarnerMedia have been exploring strategic options for the CW Network for several months, it added, quoting some people involved in the talks.
CW Network with Warner Bros has made popular shows including DC Comics' "Arrow" and its spinoff "The Flash". "Riverdale" is also among the highest grossing series of the network.
AT&T has been in the process of unwinding its expensive media investments to focus on its original business of providing phone and internet services.
It is combining WarnerMedia's media assets with Discovery to create a proposed standalone company, Warner Bros. Discovery, in a deal which is expected to close in mid-2022.
(Reporting by Baranjot Kaur in Bengaluru; Editing by Shounak Dasgupta and Rashmi Aich)