Sources told ESPN that the teams are working on trade scenarios, possibly involving four teams. The report stated that the sides are "motivated" but no deal is imminent.
Anthony's name has been rumored in trade talks for months, before the Knicks fired former president Phil Jackson. Paul was traded to Houston in June, after picking up his option with the Los Angeles Clippers.
The 32-year-old Anthony is booked for $26.2 million in 2017 and $27.9 million in 2018. He signed his five-year, $124 million contract with the Knicks in 2014. The Rockets are currently $15 million over the projected salary cap for next season.
"Wow, he will look great in this uniform," Nene posted, before deleting the post. "And I can't wait to get back on old time like in Denver with him...did you guys remember?" The post included a photo of Anthony sporting a No. 15 Rockets jersey.
Nene recently agreed to a three-year, $11 million contract with the Rockets.
An NBA source told the New York Post that the Knicks won't make a move on Anthony until the franchise has a new general manager and president in place. Sources told the Post this week that the Knicks plan on promoting Mills as their next president.
A 33-year-old Anthony could still fill that role.